1966 AHSME Problems/Problem 8
Problem
The length of the common chord of two intersecting circles is feet. If the radii are feet and feet, a possible value for the distance between the centers of the circles, expressed in feet, is:
Solution
Let be the center of the circle of radius and be the center of the circle of radius . Chord feet.
feet, since they are radii of the same circle. Hence, is isoceles with base . The height of from to is
Similarly, . Therefore, is also isoceles with base . The height of the triangle from to is
The distance between the centers of the circles (points and ) is the sum of the heights of and , which is
1966 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 7 |
Followed by Problem 9 | |
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