Engineering Board Exam Reviewer · Ptolemy's Theorem and Cyclic Quadrilaterals · medium
The angle A of a cyclic quadrilateral ABCD is 70°. Find the opposite angle C.
- 70°
- 90°
- 110°
- 20°
Answer
C. 110°
Solution
Opposite angles of a cyclic quadrilateral are supplementary: C=180°-70°=110°.
More Ptolemy's Theorem and Cyclic Quadrilaterals questions
- A cyclic quadrilateral ABCD has sides AB=6, BC=7, CD=8, and DA=5. If diagonal AC=10, find diagonal BD using Ptolemy's theorem.
- A cyclic quadrilateral ABCD has consecutive sides AB=4, BC=5, CD=6, DA=7. If diagonal AC=7.5, find diagonal BD using Ptolemy's theorem.
- A rectangle (a special cyclic quadrilateral) has sides 6 and 8. Find the length of its diagonal.
- A cyclic quadrilateral ABCD has AB=7, BC=24, CD=15, DA=20 and diagonal AC=25. Find the radius of the circumscribed circle.
- A cyclic quadrilateral has sides 9, 10, 17 and 6. Find its area.
- A cyclic quadrilateral ABCD has AB=CD=5, BC=6 and AD=14. Find the length of diagonal AC.