Problem 108

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Problem 108: (2000 AMC 12, 19)

In triangle $ABC$, $AB = 13$, $BC = 14$, $AC = 15$. Let $D$ denote the midpoint of $\overline{BC}$ and let $E$ denote the intersection of $\overline{BC}$ with the bisector of angle $BAC$. Which of the following is closest to the area of the triangle $ADE$? $\textbf {(A)}\ 2 \qquad$ $ \textbf {(B)}\ 2.5 \qquad$ $ \textbf {(C)}\ 3 \qquad$ $ \textbf {(D)}\ 3.5 \qquad$ $ \textbf {(E)}\ 4$

Solution

Exercise 108: Solution

In triangle $ABC$, $AB=10$, $BC=12$, $AC=14$. Let $D$ denote the midpoint of $\overline{BC}$ and let $E$ denote the intersection of $\overline{BC}$ with the bisector of angle $BAC$. Find the area of triangle $ADE$.

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