Ptolemy's Theorem and Cyclic Quadrilaterals — Engineering Board Exam Practice Questions

3 free engineering board exam reviewer questions on Ptolemy's Theorem and Cyclic Quadrilaterals (Plane Geometry), each with the correct answer and a worked solution.

1. 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.
2. 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.
3. A rectangle (a special cyclic quadrilateral) has sides 6 and 8. Find the length of its diagonal.