1979 AHSME Problems/Problem 12
Problem 12
In the adjoining figure, is the diameter of a semi-circle with center . Point lies on the extension of past ; point lies on the semi-circle, and is the point of intersection (distinct from ) of line segment with the semi-circle. If length equals length , and the measure of is , then the measure of is
Solution
Solution by e_power_pi_times_i
Because , triangles and are isosceles. Denote . Then , and , so . Notice that . Therefore , and .
Another Solution
Draw . Let . Since , triangle is isosceles, so . Angle is exterior to triangle , so .
Triangle is isosceles, so . Then is external to triangle , so . But , so . That means the answer is .
See also
1979 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 11 |
Followed by Problem 13 | |
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