Engineering Board Exam Reviewer · Ptolemy's Theorem and Cyclic Quadrilaterals · easy

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

1. 10
2. 14
3. 48
4. 7

Answer

A. 10

Solution

sqrt(62+82)=sqrt(100)=10. (This satisfies Ptolemy's theorem: 10×10=6×6+8×8=100.)

More Ptolemy's Theorem and Cyclic Quadrilaterals questions

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.

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