Mathematics
Geometry
A circle has radius 15 cm and a chord 6 cm long. Find the perpendicular distance from center to chord.<br/><svg xmlns="http://www.w3.org/2000/svg" width="260" height="180" viewBox="0 0 260 180" role="img"><circle cx="130" cy="95" r="65" fill="none" stroke="#1f2937" stroke-width="2"/><circle cx="130" cy="95" r="3" fill="#111"/><text x="137" y="91" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">O</text><line x1="82" y1="52" x2="185" y2="135" stroke="#2563eb" stroke-width="2.5"/><text x="72" y="47" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">A</text><text x="190" y="146" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">B</text></svg>
A. 18.7 cm
B. 12.7 cm
C. 16.7 cm
D. 14.7 cm
Correct Answer: D
Half chord=3. d=√(r²−(c/2)²)=√(216.0)≈14.7 cm.
Mathematics
Geometry
A circle has radius 14 cm and a chord 4 cm long. Find the perpendicular distance from center to chord.<br/><svg xmlns="http://www.w3.org/2000/svg" width="260" height="180" viewBox="0 0 260 180" role="img"><circle cx="130" cy="95" r="65" fill="none" stroke="#1f2937" stroke-width="2"/><circle cx="130" cy="95" r="3" fill="#111"/><text x="137" y="91" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">O</text><line x1="82" y1="52" x2="185" y2="135" stroke="#2563eb" stroke-width="2.5"/><text x="72" y="47" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">A</text><text x="190" y="146" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">B</text></svg>
A. 11.86 cm
B. 13.86 cm
C. 17.86 cm
D. 15.86 cm
Correct Answer: B
Half chord=2. d=√(r²−(c/2)²)=√(192.0)≈13.86 cm.
Mathematics
Geometry
A circle has radius 13 cm and a chord 10 cm long. Find the perpendicular distance from center to chord.<br/><svg xmlns="http://www.w3.org/2000/svg" width="260" height="180" viewBox="0 0 260 180" role="img"><circle cx="130" cy="95" r="65" fill="none" stroke="#1f2937" stroke-width="2"/><circle cx="130" cy="95" r="3" fill="#111"/><text x="137" y="91" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">O</text><line x1="82" y1="52" x2="185" y2="135" stroke="#2563eb" stroke-width="2.5"/><text x="72" y="47" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">A</text><text x="190" y="146" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">B</text></svg>
A. 12 cm
B. 16 cm
C. 10 cm
D. 14 cm
Correct Answer: A
Half chord=5. d=√(r²−(c/2)²)=√(144.0)≈12 cm.
Mathematics
Geometry
A circle has radius 12 cm and a chord 8 cm long. Find the perpendicular distance from center to chord.<br/><svg xmlns="http://www.w3.org/2000/svg" width="260" height="180" viewBox="0 0 260 180" role="img"><circle cx="130" cy="95" r="65" fill="none" stroke="#1f2937" stroke-width="2"/><circle cx="130" cy="95" r="3" fill="#111"/><text x="137" y="91" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">O</text><line x1="82" y1="52" x2="185" y2="135" stroke="#2563eb" stroke-width="2.5"/><text x="72" y="47" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">A</text><text x="190" y="146" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">B</text></svg>
A. 9.31 cm
B. 11.31 cm
C. 15.31 cm
D. 13.31 cm
Correct Answer: B
Half chord=4. d=√(r²−(c/2)²)=√(128.0)≈11.31 cm.
Mathematics
Geometry
A circle has radius 11 cm and a chord 6 cm long. Find the perpendicular distance from center to chord.<br/><svg xmlns="http://www.w3.org/2000/svg" width="260" height="180" viewBox="0 0 260 180" role="img"><circle cx="130" cy="95" r="65" fill="none" stroke="#1f2937" stroke-width="2"/><circle cx="130" cy="95" r="3" fill="#111"/><text x="137" y="91" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">O</text><line x1="82" y1="52" x2="185" y2="135" stroke="#2563eb" stroke-width="2.5"/><text x="72" y="47" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">A</text><text x="190" y="146" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">B</text></svg>
A. 12.58 cm
B. 14.58 cm
C. 10.58 cm
D. 8.58 cm
Correct Answer: C
Half chord=3. d=√(r²−(c/2)²)=√(112.0)≈10.58 cm.
Mathematics
Geometry
A circle has radius 10 cm and a chord 4 cm long. Find the perpendicular distance from center to chord.<br/><svg xmlns="http://www.w3.org/2000/svg" width="260" height="180" viewBox="0 0 260 180" role="img"><circle cx="130" cy="95" r="65" fill="none" stroke="#1f2937" stroke-width="2"/><circle cx="130" cy="95" r="3" fill="#111"/><text x="137" y="91" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">O</text><line x1="82" y1="52" x2="185" y2="135" stroke="#2563eb" stroke-width="2.5"/><text x="72" y="47" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">A</text><text x="190" y="146" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">B</text></svg>
A. 11.8 cm
B. 9.8 cm
C. 7.8 cm
D. 13.8 cm
Correct Answer: B
Half chord=2. d=√(r²−(c/2)²)=√(96.0)≈9.8 cm.
Mathematics
Geometry
A circle has radius 9 cm and a chord 10 cm long. Find the perpendicular distance from center to chord.<br/><svg xmlns="http://www.w3.org/2000/svg" width="260" height="180" viewBox="0 0 260 180" role="img"><circle cx="130" cy="95" r="65" fill="none" stroke="#1f2937" stroke-width="2"/><circle cx="130" cy="95" r="3" fill="#111"/><text x="137" y="91" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">O</text><line x1="82" y1="52" x2="185" y2="135" stroke="#2563eb" stroke-width="2.5"/><text x="72" y="47" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">A</text><text x="190" y="146" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">B</text></svg>
A. 9.48 cm
B. 7.48 cm
C. 5.48 cm
D. 11.48 cm
Correct Answer: B
Half chord=5. d=√(r²−(c/2)²)=√(56.0)≈7.48 cm.
Mathematics
Geometry
A circle has radius 8 cm and a chord 8 cm long. Find the perpendicular distance from center to chord.<br/><svg xmlns="http://www.w3.org/2000/svg" width="260" height="180" viewBox="0 0 260 180" role="img"><circle cx="130" cy="95" r="65" fill="none" stroke="#1f2937" stroke-width="2"/><circle cx="130" cy="95" r="3" fill="#111"/><text x="137" y="91" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">O</text><line x1="82" y1="52" x2="185" y2="135" stroke="#2563eb" stroke-width="2.5"/><text x="72" y="47" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">A</text><text x="190" y="146" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">B</text></svg>
A. 8.93 cm
B. 6.93 cm
C. 4.93 cm
D. 10.93 cm
Correct Answer: B
Half chord=4. d=√(r²−(c/2)²)=√(48.0)≈6.93 cm.
Mathematics
Geometry
A circle has radius 7 cm and a chord 6 cm long. Find the perpendicular distance from center to chord.<br/><svg xmlns="http://www.w3.org/2000/svg" width="260" height="180" viewBox="0 0 260 180" role="img"><circle cx="130" cy="95" r="65" fill="none" stroke="#1f2937" stroke-width="2"/><circle cx="130" cy="95" r="3" fill="#111"/><text x="137" y="91" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">O</text><line x1="82" y1="52" x2="185" y2="135" stroke="#2563eb" stroke-width="2.5"/><text x="72" y="47" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">A</text><text x="190" y="146" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">B</text></svg>
A. 4.32 cm
B. 10.32 cm
C. 8.32 cm
D. 6.32 cm
Correct Answer: D
Half chord=3. d=√(r²−(c/2)²)=√(40.0)≈6.32 cm.
Mathematics
Geometry
A circle has radius 6 cm and a chord 4 cm long. Find the perpendicular distance from center to chord.<br/><svg xmlns="http://www.w3.org/2000/svg" width="260" height="180" viewBox="0 0 260 180" role="img"><circle cx="130" cy="95" r="65" fill="none" stroke="#1f2937" stroke-width="2"/><circle cx="130" cy="95" r="3" fill="#111"/><text x="137" y="91" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">O</text><line x1="82" y1="52" x2="185" y2="135" stroke="#2563eb" stroke-width="2.5"/><text x="72" y="47" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">A</text><text x="190" y="146" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">B</text></svg>
A. 3.66 cm
B. 5.66 cm
C. 9.66 cm
D. 7.66 cm
Correct Answer: B
Half chord=2. d=√(r²−(c/2)²)=√(32.0)≈5.66 cm.
Mathematics
Geometry
Equal chords subtend:<br/><svg xmlns="http://www.w3.org/2000/svg" width="260" height="180" viewBox="0 0 260 180" role="img"><circle cx="130" cy="95" r="65" fill="none" stroke="#1f2937" stroke-width="2"/><circle cx="130" cy="95" r="3" fill="#111"/><text x="137" y="91" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">O</text><line x1="82" y1="52" x2="185" y2="135" stroke="#2563eb" stroke-width="2.5"/><text x="72" y="47" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">A</text><text x="190" y="146" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">B</text></svg>
A. 180°
B. Secant
C. Radius
D. Equal angles
Correct Answer: D
Correct circle theorem/definition: Equal angles.<br/><svg xmlns="http://www.w3.org/2000/svg" width="260" height="180" viewBox="0 0 260 180" role="img"><circle cx="130" cy="95" r="65" fill="none" stroke="#1f2937" stroke-width="2"/><circle cx="130" cy="95" r="3" fill="#111"/><text x="137" y="91" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">O</text><line x1="82" y1="52" x2="185" y2="135" stroke="#2563eb" stroke-width="2.5"/><text x="72" y="47" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">A</text><text x="190" y="146" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">B</text></svg>
Mathematics
Geometry
Opposite angles of a cyclic quadrilateral are:<br/><svg xmlns="http://www.w3.org/2000/svg" width="260" height="180" viewBox="0 0 260 180" role="img"><circle cx="130" cy="95" r="65" fill="none" stroke="#1f2937" stroke-width="2"/><circle cx="130" cy="95" r="3" fill="#111"/><text x="137" y="91" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">O</text></svg>
A. Radius
B. 180°
C. Supplementary
D. Secant
Correct Answer: C
Correct circle theorem/definition: Supplementary.<br/><svg xmlns="http://www.w3.org/2000/svg" width="260" height="180" viewBox="0 0 260 180" role="img"><circle cx="130" cy="95" r="65" fill="none" stroke="#1f2937" stroke-width="2"/><circle cx="130" cy="95" r="3" fill="#111"/><text x="137" y="91" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">O</text></svg>
Mathematics
Geometry
Angle in a semicircle is:<br/><svg xmlns="http://www.w3.org/2000/svg" width="260" height="180" viewBox="0 0 260 180" role="img"><circle cx="130" cy="95" r="65" fill="none" stroke="#1f2937" stroke-width="2"/><circle cx="130" cy="95" r="3" fill="#111"/><text x="137" y="91" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">O</text></svg>
A. 90°
B. Secant
C. Radius
D. 180°
Correct Answer: A
Correct circle theorem/definition: 90°.<br/><svg xmlns="http://www.w3.org/2000/svg" width="260" height="180" viewBox="0 0 260 180" role="img"><circle cx="130" cy="95" r="65" fill="none" stroke="#1f2937" stroke-width="2"/><circle cx="130" cy="95" r="3" fill="#111"/><text x="137" y="91" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">O</text></svg>
Mathematics
Geometry
Angles in same segment are:<br/><svg xmlns="http://www.w3.org/2000/svg" width="260" height="180" viewBox="0 0 260 180" role="img"><circle cx="130" cy="95" r="65" fill="none" stroke="#1f2937" stroke-width="2"/><circle cx="130" cy="95" r="3" fill="#111"/><text x="137" y="91" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">O</text></svg>
A. 180°
B. Secant
C. Equal
D. Radius
Correct Answer: C
Correct circle theorem/definition: Equal.<br/><svg xmlns="http://www.w3.org/2000/svg" width="260" height="180" viewBox="0 0 260 180" role="img"><circle cx="130" cy="95" r="65" fill="none" stroke="#1f2937" stroke-width="2"/><circle cx="130" cy="95" r="3" fill="#111"/><text x="137" y="91" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">O</text></svg>
Mathematics
Geometry
Radius to tangent point is:<br/><svg xmlns="http://www.w3.org/2000/svg" width="260" height="180" viewBox="0 0 260 180" role="img"><circle cx="130" cy="95" r="65" fill="none" stroke="#1f2937" stroke-width="2"/><circle cx="130" cy="95" r="3" fill="#111"/><text x="137" y="91" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">O</text><line x1="195" y1="20" x2="195" y2="165" stroke="#dc2626" stroke-width="2.5"/><line x1="130" y1="95" x2="195" y2="95" stroke="#6b7280" stroke-width="1.5"/><rect x="185" y="95" width="10" height="10" fill="none" stroke="#dc2626"/></svg>
A. 180°
B. Radius
C. Secant
D. Perpendicular to tangent
Correct Answer: D
Correct circle theorem/definition: Perpendicular to tangent.<br/><svg xmlns="http://www.w3.org/2000/svg" width="260" height="180" viewBox="0 0 260 180" role="img"><circle cx="130" cy="95" r="65" fill="none" stroke="#1f2937" stroke-width="2"/><circle cx="130" cy="95" r="3" fill="#111"/><text x="137" y="91" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">O</text><line x1="195" y1="20" x2="195" y2="165" stroke="#dc2626" stroke-width="2.5"/><line x1="130" y1="95" x2="195" y2="95" stroke="#6b7280" stroke-width="1.5"/><rect x="185" y="95" width="10" height="10" fill="none" stroke="#dc2626"/></svg>
Mathematics
Geometry
Longest chord:<br/><svg xmlns="http://www.w3.org/2000/svg" width="260" height="180" viewBox="0 0 260 180" role="img"><circle cx="130" cy="95" r="65" fill="none" stroke="#1f2937" stroke-width="2"/><circle cx="130" cy="95" r="3" fill="#111"/><text x="137" y="91" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">O</text><line x1="82" y1="52" x2="185" y2="135" stroke="#2563eb" stroke-width="2.5"/><text x="72" y="47" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">A</text><text x="190" y="146" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">B</text></svg>
A. Secant
B. Radius
C. 180°
D. Diameter
Correct Answer: D
Correct circle theorem/definition: Diameter.<br/><svg xmlns="http://www.w3.org/2000/svg" width="260" height="180" viewBox="0 0 260 180" role="img"><circle cx="130" cy="95" r="65" fill="none" stroke="#1f2937" stroke-width="2"/><circle cx="130" cy="95" r="3" fill="#111"/><text x="137" y="91" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">O</text><line x1="82" y1="52" x2="185" y2="135" stroke="#2563eb" stroke-width="2.5"/><text x="72" y="47" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">A</text><text x="190" y="146" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">B</text></svg>
Mathematics
Geometry
Line cutting at two points:<br/><svg xmlns="http://www.w3.org/2000/svg" width="260" height="180" viewBox="0 0 260 180" role="img"><circle cx="130" cy="95" r="65" fill="none" stroke="#1f2937" stroke-width="2"/><circle cx="130" cy="95" r="3" fill="#111"/><text x="137" y="91" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">O</text></svg>
A. Secant
B. 180°
C. None of these
D. Radius
Correct Answer: A
Correct circle theorem/definition: Secant.<br/><svg xmlns="http://www.w3.org/2000/svg" width="260" height="180" viewBox="0 0 260 180" role="img"><circle cx="130" cy="95" r="65" fill="none" stroke="#1f2937" stroke-width="2"/><circle cx="130" cy="95" r="3" fill="#111"/><text x="137" y="91" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">O</text></svg>
Mathematics
Geometry
Line touching at one point:<br/><svg xmlns="http://www.w3.org/2000/svg" width="260" height="180" viewBox="0 0 260 180" role="img"><circle cx="130" cy="95" r="65" fill="none" stroke="#1f2937" stroke-width="2"/><circle cx="130" cy="95" r="3" fill="#111"/><text x="137" y="91" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">O</text><line x1="195" y1="20" x2="195" y2="165" stroke="#dc2626" stroke-width="2.5"/><line x1="130" y1="95" x2="195" y2="95" stroke="#6b7280" stroke-width="1.5"/><rect x="185" y="95" width="10" height="10" fill="none" stroke="#dc2626"/></svg>
A. 180°
B. Secant
C. Tangent
D. Radius
Correct Answer: C
Correct circle theorem/definition: Tangent.<br/><svg xmlns="http://www.w3.org/2000/svg" width="260" height="180" viewBox="0 0 260 180" role="img"><circle cx="130" cy="95" r="65" fill="none" stroke="#1f2937" stroke-width="2"/><circle cx="130" cy="95" r="3" fill="#111"/><text x="137" y="91" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">O</text><line x1="195" y1="20" x2="195" y2="165" stroke="#dc2626" stroke-width="2.5"/><line x1="130" y1="95" x2="195" y2="95" stroke="#6b7280" stroke-width="1.5"/><rect x="185" y="95" width="10" height="10" fill="none" stroke="#dc2626"/></svg>
Mathematics
Geometry
Chord through center:<br/><svg xmlns="http://www.w3.org/2000/svg" width="260" height="180" viewBox="0 0 260 180" role="img"><circle cx="130" cy="95" r="65" fill="none" stroke="#1f2937" stroke-width="2"/><circle cx="130" cy="95" r="3" fill="#111"/><text x="137" y="91" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">O</text><line x1="82" y1="52" x2="185" y2="135" stroke="#2563eb" stroke-width="2.5"/><text x="72" y="47" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">A</text><text x="190" y="146" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">B</text></svg>
A. 180°
B. Secant
C. Diameter
D. Radius
Correct Answer: C
Correct circle theorem/definition: Diameter.<br/><svg xmlns="http://www.w3.org/2000/svg" width="260" height="180" viewBox="0 0 260 180" role="img"><circle cx="130" cy="95" r="65" fill="none" stroke="#1f2937" stroke-width="2"/><circle cx="130" cy="95" r="3" fill="#111"/><text x="137" y="91" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">O</text><line x1="82" y1="52" x2="185" y2="135" stroke="#2563eb" stroke-width="2.5"/><text x="72" y="47" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">A</text><text x="190" y="146" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">B</text></svg>
Mathematics
Geometry
Segment from center to circle:<br/><svg xmlns="http://www.w3.org/2000/svg" width="260" height="180" viewBox="0 0 260 180" role="img"><circle cx="130" cy="95" r="65" fill="none" stroke="#1f2937" stroke-width="2"/><circle cx="130" cy="95" r="3" fill="#111"/><text x="137" y="91" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">O</text></svg>
A. Secant
B. 180°
C. Radius
D. None of these
Correct Answer: C
Correct circle theorem/definition: Radius.<br/><svg xmlns="http://www.w3.org/2000/svg" width="260" height="180" viewBox="0 0 260 180" role="img"><circle cx="130" cy="95" r="65" fill="none" stroke="#1f2937" stroke-width="2"/><circle cx="130" cy="95" r="3" fill="#111"/><text x="137" y="91" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">O</text></svg>