1980 AHSME Problems/Problem 23
Problem
Line segments drawn from the vertex opposite the hypotenuse of a right triangle to the points trisecting the hypotenuse have lengths and , where is a real number such that . The length of the hypotenuse is
Solution
Consider right triangle with hypotenuse . Let points and trisect . WLOG, let and (the proof works the other way around as well).
Applying Stewart's theorem on with point , we obtain the equation
Similarly using point , we obtain
Adding these equations, we get
As the other 2 answers yield degenerate triangles, we see that the answer is
See also
1980 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 22 |
Followed by Problem 24 | |
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