Problem 144

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Problem 144: (2002 AMC 10A, 23)

Points $A,B,C$ and $D$ lie on a line, in that order, with $AB = CD$ and $BC = 12$. Point $E$ is not on the line, and $BE = CE = 10$. The perimeter of $\triangle AED$ is twice the perimeter of $\triangle BEC$. Find $AB$. $\text{(A)}\ 15/2 \qquad$ $ \text{(B)}\ 8 \qquad$ $ \text{(C)}\ 17/2 \qquad$ $ \text{(D)}\ 9 \qquad$ $ \text{(E)}\ 19/2$

Solution

Exercise 144: Solution

Points $A,B,C$ and $D$ lie on a line, in that order, with $AB=CD$ and $BC=10$. Point $E$ is not on the line, and $BE=CE=13$. The perimeter of $\triangle AED$ is twice the perimeter of $\triangle BEC$. Find $AB$.

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