Mathematics
Geometry
Circle radius 9 cm, chord 12 cm. Find 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. 8.71 cm
B. 4.71 cm
C. 10.71 cm
D. 6.71 cm
Correct Answer: D
Half-chord=6; d=√(9²−6²)=√45≈6.71 cm.
Mathematics
Geometry
Circle radius 8 cm, chord 10 cm. Find 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. 10.24 cm
B. 6.24 cm
C. 8.24 cm
D. 4.24 cm
Correct Answer: B
Half-chord=5; d=√(8²−5²)=√39≈6.24 cm.
Mathematics
Geometry
Circle radius 7 cm, chord 8 cm. Find 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. 3.74 cm
B. 9.74 cm
C. 7.74 cm
D. 5.74 cm
Correct Answer: D
Half-chord=4; d=√(7²−4²)=√33≈5.74 cm.
Mathematics
Geometry
Circle radius 6 cm, chord 6 cm. Find 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. 7.2 cm
B. 9.2 cm
C. 5.2 cm
D. 3.2 cm
Correct Answer: C
Half-chord=3; d=√(6²−3²)=√27≈5.2 cm.
Mathematics
Geometry
Circle radius 5 cm, chord 4 cm. Find 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. 8.58 cm
B. 4.58 cm
C. 6.58 cm
D. 2.58 cm
Correct Answer: B
Half-chord=2; d=√(5²−2²)=√21≈4.58 cm.
Mathematics
Geometry
A regular polygon has exterior angle 6°. How many sides?
A. 58
B. 64
C. 60
D. 62
Correct Answer: C
n=360°/6°=60.
Mathematics
Geometry
A regular polygon has exterior angle 8°. How many sides?
A. 45
B. 49
C. 47
D. 43
Correct Answer: A
n=360°/8°=45.
Mathematics
Geometry
A regular polygon has exterior angle 9°. How many sides?
A. 38
B. 42
C. 44
D. 40
Correct Answer: D
n=360°/9°=40.
Mathematics
Geometry
A regular polygon has exterior angle 10°. How many sides?
A. 34
B. 38
C. 40
D. 36
Correct Answer: D
n=360°/10°=36.
Mathematics
Geometry
A regular polygon has exterior angle 12°. How many sides?
A. 28
B. 34
C. 30
D. 32
Correct Answer: C
n=360°/12°=30.
Mathematics
Geometry
A regular polygon has exterior angle 15°. How many sides?
A. 22
B. 26
C. 24
D. 28
Correct Answer: C
n=360°/15°=24.
Mathematics
Geometry
A regular polygon has exterior angle 18°. How many sides?
A. 22
B. 20
C. 18
D. 24
Correct Answer: B
n=360°/18°=20.
Mathematics
Geometry
A regular polygon has exterior angle 20°. How many sides?
A. 20
B. 18
C. 22
D. 16
Correct Answer: B
n=360°/20°=18.
Mathematics
Geometry
A regular polygon has exterior angle 24°. How many sides?
A. 13
B. 15
C. 19
D. 17
Correct Answer: B
n=360°/24°=15.
Mathematics
Geometry
A regular polygon has exterior angle 30°. How many sides?
A. 14
B. 16
C. 10
D. 12
Correct Answer: D
n=360°/30°=12.
Mathematics
Geometry
A regular polygon has exterior angle 36°. How many sides?
A. 14
B. 10
C. 12
D. 8
Correct Answer: B
n=360°/36°=10.
Mathematics
Geometry
A regular polygon has exterior angle 40°. How many sides?
A. 11
B. 7
C. 13
D. 9
Correct Answer: D
n=360°/40°=9.
Mathematics
Geometry
A regular polygon has exterior angle 45°. How many sides?
A. 6
B. 12
C. 8
D. 10
Correct Answer: C
n=360°/45°=8.
Mathematics
Geometry
A regular polygon has exterior angle 60°. How many sides?
A. 4
B. 6
C. 10
D. 8
Correct Answer: B
n=360°/60°=6.
Mathematics
Geometry
A regular polygon has exterior angle 72°. How many sides?
A. 9
B. 3
C. 5
D. 7
Correct Answer: C
n=360°/72°=5.