1991 AIME Problems/Problem 14
Problem
A hexagon is inscribed in a circle. Five of the sides have length and the sixth, denoted by , has length . Find the sum of the lengths of the three diagonals that can be drawn from .
Solution
Let , , and .
Ptolemy's Theorem on gives , and Ptolemy on gives . Subtracting these equations give , and from this . Ptolemy on gives , and from this . Finally, plugging back into the first equation gives , so .
Video Solution by OmegaLearn
https://youtu.be/DVuf-uXjfzY?t=522
~ pi_is_3.14
See also
1991 AIME (Problems • Answer Key • Resources) | ||
Preceded by Problem 13 |
Followed by Problem 15 | |
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