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

A cyclic quadrilateral ABCD has AB=7, BC=24, CD=15, DA=20 and diagonal AC=25. Find the radius of the circumscribed circle.

  1. 25
  2. 12.5
  3. 10
  4. 15

Answer

B. 12.5

Solution

Since 72+242=252 and 152+202=252, angles B and D are right angles, so AC is a diameter and R=25/2=12.5.

More Ptolemy's Theorem and Cyclic Quadrilaterals questions

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  4. 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.
  5. 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.
  6. A rectangle (a special cyclic quadrilateral) has sides 6 and 8. Find the length of its diagonal.

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