1961 AHSME Problems/Problem 31
Problem
In the ratio is . The bisector of the exterior angle at intersects extended at ( is between and ). The ratio is:
Solution
Let and . Draw , where is on and . By AA Similarity, , so , , and .
Also, let and . Since the angles of a triangle add up to , . By Exterior Angle Theorem, , and since bisects , . Because , . Thus, , making an isosceles triangle.
Because is isosceles, , so . That means , so . Thus, , so . The answer is , and it can be verified (or obtained) by making a 3-4-5 right triangle.
See Also
1961 AHSC (Problems • Answer Key • Resources) | ||
Preceded by Problem 30 |
Followed by Problem 32 | |
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