1953 AHSME Problems/Problem 42
Problem
The centers of two circles are inches apart. The smaller circle has a radius of inches and the larger one has a radius of inches. The length of the common internal tangent is:
Solution
Let be the center of the circle with radius , and be the center of the circle with radius . Let be the common internal tangent of circle and circle . Extend past to point such that . Since and , is a rectangle. Therefore, and .
Since the centers of the two circles are inches apart, . Also, . Using the Pythagorean Theorem on right triangle , . The length of the common internal tangent is
See Also
1953 AHSC (Problems • Answer Key • Resources) | ||
Preceded by Problem 41 |
Followed by Problem 43 | |
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