Mathematics
Geometry
A circle has radius 17 cm. At point T a tangent is drawn. What angle does radius OT make with the tangent at T?<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="130" y1="95" x2="195" y2="95" stroke="#2563eb" stroke-width="2.5"/><text x="153" y="85" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">r=17</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. 90°
B. 75°
C. 120°
D. 105°
Correct Answer: A
A radius to the point of tangency is perpendicular to the tangent, so ∠OT(tangent)=90°.
Mathematics
Geometry
A circle has radius 16 cm. At point T a tangent is drawn. What angle does radius OT make with the tangent at T?<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="130" y1="95" x2="195" y2="95" stroke="#2563eb" stroke-width="2.5"/><text x="153" y="85" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">r=16</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. 75°
B. 105°
C. 90°
D. 120°
Correct Answer: C
A radius to the point of tangency is perpendicular to the tangent, so ∠OT(tangent)=90°.
Mathematics
Geometry
A circle has radius 15 cm. At point T a tangent is drawn. What angle does radius OT make with the tangent at T?<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="130" y1="95" x2="195" y2="95" stroke="#2563eb" stroke-width="2.5"/><text x="153" y="85" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">r=15</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. 120°
B. 105°
C. 90°
D. 75°
Correct Answer: C
A radius to the point of tangency is perpendicular to the tangent, so ∠OT(tangent)=90°.
Mathematics
Geometry
A circle has radius 14 cm. At point T a tangent is drawn. What angle does radius OT make with the tangent at T?<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="130" y1="95" x2="195" y2="95" stroke="#2563eb" stroke-width="2.5"/><text x="153" y="85" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">r=14</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. 105°
B. 90°
C. 120°
D. 75°
Correct Answer: B
A radius to the point of tangency is perpendicular to the tangent, so ∠OT(tangent)=90°.
Mathematics
Geometry
A circle has radius 13 cm. At point T a tangent is drawn. What angle does radius OT make with the tangent at T?<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="130" y1="95" x2="195" y2="95" stroke="#2563eb" stroke-width="2.5"/><text x="153" y="85" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">r=13</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. 75°
B. 120°
C. 105°
D. 90°
Correct Answer: D
A radius to the point of tangency is perpendicular to the tangent, so ∠OT(tangent)=90°.
Mathematics
Geometry
A circle has radius 12 cm. At point T a tangent is drawn. What angle does radius OT make with the tangent at T?<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="130" y1="95" x2="195" y2="95" stroke="#2563eb" stroke-width="2.5"/><text x="153" y="85" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">r=12</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. 90°
B. 75°
C. 120°
D. 105°
Correct Answer: A
A radius to the point of tangency is perpendicular to the tangent, so ∠OT(tangent)=90°.
Mathematics
Geometry
A circle has radius 11 cm. At point T a tangent is drawn. What angle does radius OT make with the tangent at T?<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="130" y1="95" x2="195" y2="95" stroke="#2563eb" stroke-width="2.5"/><text x="153" y="85" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">r=11</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. 75°
B. 90°
C. 105°
D. 120°
Correct Answer: B
A radius to the point of tangency is perpendicular to the tangent, so ∠OT(tangent)=90°.
Mathematics
Geometry
A circle has radius 10 cm. At point T a tangent is drawn. What angle does radius OT make with the tangent at T?<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="130" y1="95" x2="195" y2="95" stroke="#2563eb" stroke-width="2.5"/><text x="153" y="85" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">r=10</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. 90°
B. 75°
C. 120°
D. 105°
Correct Answer: A
A radius to the point of tangency is perpendicular to the tangent, so ∠OT(tangent)=90°.
Mathematics
Geometry
A circle has radius 9 cm. At point T a tangent is drawn. What angle does radius OT make with the tangent at T?<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="130" y1="95" x2="195" y2="95" stroke="#2563eb" stroke-width="2.5"/><text x="153" y="85" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">r=9</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. 120°
B. 75°
C. 90°
D. 105°
Correct Answer: C
A radius to the point of tangency is perpendicular to the tangent, so ∠OT(tangent)=90°.
Mathematics
Geometry
A circle has radius 8 cm. At point T a tangent is drawn. What angle does radius OT make with the tangent at T?<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="130" y1="95" x2="195" y2="95" stroke="#2563eb" stroke-width="2.5"/><text x="153" y="85" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">r=8</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. 105°
B. 120°
C. 90°
D. 75°
Correct Answer: C
A radius to the point of tangency is perpendicular to the tangent, so ∠OT(tangent)=90°.
Mathematics
Geometry
A circle has radius 7 cm. At point T a tangent is drawn. What angle does radius OT make with the tangent at T?<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="130" y1="95" x2="195" y2="95" stroke="#2563eb" stroke-width="2.5"/><text x="153" y="85" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">r=7</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. 120°
B. 105°
C. 90°
D. 75°
Correct Answer: C
A radius to the point of tangency is perpendicular to the tangent, so ∠OT(tangent)=90°.
Mathematics
Geometry
A circle has radius 6 cm. At point T a tangent is drawn. What angle does radius OT make with the tangent at T?<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="130" y1="95" x2="195" y2="95" stroke="#2563eb" stroke-width="2.5"/><text x="153" y="85" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">r=6</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. 120°
B. 90°
C. 75°
D. 105°
Correct Answer: B
A radius to the point of tangency is perpendicular to the tangent, so ∠OT(tangent)=90°.
Mathematics
Geometry
A circle has radius 5 cm. At point T a tangent is drawn. What angle does radius OT make with the tangent at T?<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="130" y1="95" x2="195" y2="95" stroke="#2563eb" stroke-width="2.5"/><text x="153" y="85" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">r=5</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. 105°
B. 90°
C. 120°
D. 75°
Correct Answer: B
A radius to the point of tangency is perpendicular to the tangent, so ∠OT(tangent)=90°.
Mathematics
Geometry
A circle has radius 4 cm. At point T a tangent is drawn. What angle does radius OT make with the tangent at T?<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="130" y1="95" x2="195" y2="95" stroke="#2563eb" stroke-width="2.5"/><text x="153" y="85" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">r=4</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. 90°
B. 105°
C. 75°
D. 120°
Correct Answer: A
A radius to the point of tangency is perpendicular to the tangent, so ∠OT(tangent)=90°.
Mathematics
Geometry
A circle has radius 3 cm. At point T a tangent is drawn. What angle does radius OT make with the tangent at T?<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="130" y1="95" x2="195" y2="95" stroke="#2563eb" stroke-width="2.5"/><text x="153" y="85" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">r=3</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. 75°
B. 120°
C. 105°
D. 90°
Correct Answer: D
A radius to the point of tangency is perpendicular to the tangent, so ∠OT(tangent)=90°.
Mathematics
Geometry
ABCD is cyclic. If ∠A=112°, find opposite ∠C.<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. 84°
B. 68°
C. 76°
D. 60°
Correct Answer: B
Opposite cyclic angles are supplementary: ∠C=180°−112°=68°.
Mathematics
Geometry
ABCD is cyclic. If ∠A=109°, find opposite ∠C.<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. 79°
B. 71°
C. 63°
D. 87°
Correct Answer: B
Opposite cyclic angles are supplementary: ∠C=180°−109°=71°.
Mathematics
Geometry
ABCD is cyclic. If ∠A=106°, find opposite ∠C.<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. 74°
B. 82°
C. 90°
D. 66°
Correct Answer: A
Opposite cyclic angles are supplementary: ∠C=180°−106°=74°.
Mathematics
Geometry
ABCD is cyclic. If ∠A=103°, find opposite ∠C.<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. 69°
B. 85°
C. 77°
D. 93°
Correct Answer: C
Opposite cyclic angles are supplementary: ∠C=180°−103°=77°.
Mathematics
Geometry
ABCD is cyclic. If ∠A=100°, find opposite ∠C.<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. 88°
B. 72°
C. 96°
D. 80°
Correct Answer: D
Opposite cyclic angles are supplementary: ∠C=180°−100°=80°.