1960 AHSME Problems/Problem 40
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Problem
Given right with legs . Find the length of the shorter angle trisector from to the hypotenuse:
Solution
Angle is split into three angles. The shorter angle trisector will be the one closer . Let it intersect at point . Let the perpendicular from point intersect at point and have length . Thus is a triangle and has length . Because is similar to , has length . The problem asks for the length of , or . Solving for and multiplying by two gives .
See Also
1960 AHSC (Problems • Answer Key • Resources) | ||
Preceded by Problem 39 |
Followed by 1961 AHSME | |
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All AHSME Problems and Solutions |