Engineering Board Exam Reviewer · Ptolemy's Theorem and Cyclic Quadrilaterals · medium
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.
- 8.3
- 9.1
- 7.5
- 8.8
Answer
A. 8.3
Solution
Ptolemy's theorem: AC· BD=AB· CD+BC· DA=6(8)+7(5)=48+35=83 BD=8.3.
More Ptolemy's Theorem and Cyclic Quadrilaterals questions
- 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.
- The angle A of a cyclic quadrilateral ABCD is 70°. Find the opposite angle C.