Problem 223

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Problem 223: (2014 AMC 12b, 24)

Let $ABCDE$ be a pentagon inscribed in a circle such that $AB = CD = 3$, $BC = DE = 10$, and $AE= 14$. The sum of the lengths of all diagonals of $ABCDE$ is equal to $\frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. What is $m+n$ ? $\textbf{(A) }129\qquad$ $ \textbf{(B) }247\qquad$ $ \textbf{(C) }353\qquad$ $ \textbf{(D) }391\qquad$ $ \textbf{(E) }421\qquad$

Solution

Exercise 223: Solution

Let $ABCDE$ be a pentagon inscribed in a circle with $AB=CD=5,BC=DE=12,AE=14$. The sum of the lengths of all diagonals is $\frac mn$. What is $m+n$?

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