2009 AIME I Problems/Problem 5
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Problem
Triangle has and . Points and are located on and respectively so that , and is the angle bisector of angle . Let be the point of intersection of and , and let be the point on line for which is the midpoint of . If , find .
Solution
Since is the midpoint of and , quadrilateral is a parallelogram, which implies and is similar to
Thus,
Now lets apply the angle bisector theorem.
See also
2009 AIME I (Problems • Answer Key • Resources) | ||
Preceded by Problem 4 |
Followed by Problem 6 | |
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