1992 AHSME Problems/Problem 30
Problem
Let be an isosceles trapezoid with bases and . Suppose and a circle with center on is tangent to segments and . If is the smallest possible value of , then =
Solution
Note that the center of the circle is the midpoint of , call it . When we decrease , the limiting condition is that the circle will eventually be tangent to segment at and segment at . That is, and .
From here, we drop the altitude from to ; call the base . Since , we have Thus, . Furthermore,
See also
1992 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 29 |
Followed by Problem 30 | |
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