CSS - PMS - CCE - PCS - Mathematics
Geometry
ABCD is cyclic. If ∠A=97°, 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. 83°
B. 99°
C. 75°
D. 91°
Correct Answer: A
Opposite cyclic angles are supplementary: ∠C=180°−97°=83°.
CSS - PMS - CCE - PCS - Mathematics
Geometry
ABCD is cyclic. If ∠A=94°, 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. 94°
B. 78°
C. 86°
D. 102°
Correct Answer: C
Opposite cyclic angles are supplementary: ∠C=180°−94°=86°.
CSS - PMS - CCE - PCS - Mathematics
Geometry
ABCD is cyclic. If ∠A=91°, 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. 89°
B. 105°
C. 97°
D. 81°
Correct Answer: A
Opposite cyclic angles are supplementary: ∠C=180°−91°=89°.
CSS - PMS - CCE - PCS - Mathematics
Geometry
ABCD is cyclic. If ∠A=88°, 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. 100°
C. 92°
D. 108°
Correct Answer: C
Opposite cyclic angles are supplementary: ∠C=180°−88°=92°.
CSS - PMS - CCE - PCS - Mathematics
Geometry
ABCD is cyclic. If ∠A=85°, 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. 95°
B. 87°
C. 111°
D. 103°
Correct Answer: A
Opposite cyclic angles are supplementary: ∠C=180°−85°=95°.
CSS - PMS - CCE - PCS - Mathematics
Geometry
ABCD is cyclic. If ∠A=82°, 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. 114°
B. 106°
C. 98°
D. 90°
Correct Answer: C
Opposite cyclic angles are supplementary: ∠C=180°−82°=98°.
CSS - PMS - CCE - PCS - Mathematics
Geometry
ABCD is cyclic. If ∠A=79°, 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. 93°
B. 109°
C. 101°
D. 117°
Correct Answer: C
Opposite cyclic angles are supplementary: ∠C=180°−79°=101°.
CSS - PMS - CCE - PCS - Mathematics
Geometry
ABCD is cyclic. If ∠A=76°, 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. 120°
B. 96°
C. 112°
D. 104°
Correct Answer: D
Opposite cyclic angles are supplementary: ∠C=180°−76°=104°.
CSS - PMS - CCE - PCS - Mathematics
Geometry
ABCD is cyclic. If ∠A=73°, 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. 115°
B. 99°
C. 123°
D. 107°
Correct Answer: D
Opposite cyclic angles are supplementary: ∠C=180°−73°=107°.
CSS - PMS - CCE - PCS - Mathematics
Geometry
ABCD is cyclic. If ∠A=70°, 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. 110°
B. 102°
C. 118°
D. 126°
Correct Answer: A
Opposite cyclic angles are supplementary: ∠C=180°−70°=110°.
CSS - PMS - CCE - PCS - Mathematics
Geometry
AD bisects ∠A. AB=10, AC=11, BD=6. Find DC.
A. 10.6
B. 6.6
C. 4.6
D. 8.6
Correct Answer: B
Angle-bisector theorem: BD/DC=AB/AC, so DC=6.6.
CSS - PMS - CCE - PCS - Mathematics
Geometry
AD bisects ∠A. AB=9, AC=10, BD=5. Find DC.
A. 3.56
B. 7.56
C. 9.56
D. 5.56
Correct Answer: D
Angle-bisector theorem: BD/DC=AB/AC, so DC=5.56.
CSS - PMS - CCE - PCS - Mathematics
Geometry
AD bisects ∠A. AB=8, AC=9, BD=4. Find DC.
A. 8.5
B. 2.5
C. 6.5
D. 4.5
Correct Answer: D
Angle-bisector theorem: BD/DC=AB/AC, so DC=4.5.
CSS - PMS - CCE - PCS - Mathematics
Geometry
AD bisects ∠A. AB=7, AC=14, BD=7. Find DC.
A. 18
B. 14
C. 12
D. 16
Correct Answer: B
Angle-bisector theorem: BD/DC=AB/AC, so DC=14.
CSS - PMS - CCE - PCS - Mathematics
Geometry
AD bisects ∠A. AB=6, AC=13, BD=6. Find DC.
A. 17
B. 15
C. 13
D. 11
Correct Answer: C
Angle-bisector theorem: BD/DC=AB/AC, so DC=13.
CSS - PMS - CCE - PCS - Mathematics
Geometry
AD bisects ∠A. AB=10, AC=12, BD=5. Find DC.
A. 10
B. 6
C. 4
D. 8
Correct Answer: B
Angle-bisector theorem: BD/DC=AB/AC, so DC=6.
CSS - PMS - CCE - PCS - Mathematics
Geometry
AD bisects ∠A. AB=9, AC=11, BD=4. Find DC.
A. 2.89
B. 6.89
C. 4.89
D. 8.89
Correct Answer: C
Angle-bisector theorem: BD/DC=AB/AC, so DC=4.89.
CSS - PMS - CCE - PCS - Mathematics
Geometry
AD bisects ∠A. AB=8, AC=10, BD=7. Find DC.
A. 12.75
B. 6.75
C. 8.75
D. 10.75
Correct Answer: C
Angle-bisector theorem: BD/DC=AB/AC, so DC=8.75.
CSS - PMS - CCE - PCS - Mathematics
Geometry
AD bisects ∠A. AB=7, AC=9, BD=6. Find DC.
A. 7.71
B. 5.71
C. 11.71
D. 9.71
Correct Answer: A
Angle-bisector theorem: BD/DC=AB/AC, so DC=7.71.
CSS - PMS - CCE - PCS - Mathematics
Geometry
AD bisects ∠A. AB=6, AC=14, BD=5. Find DC.
A. 11.67
B. 13.67
C. 9.67
D. 15.67
Correct Answer: A
Angle-bisector theorem: BD/DC=AB/AC, so DC=11.67.