1954 AHSME Problems/Problem 39
The locus of the midpoint of a line segment that is drawn from a given external point to a given circle with center and radius , is:
Solution
Note that the midpoint of to the point is the image of under a homothety of factor with center . Since homotheties preserve circles, the image of the midpoint as varies over the circle is a circle centered at the midpoint of and the original center and radius half the original radius. Therefore, our answer is , and we are done.
See Also
1954 AHSC (Problems • Answer Key • Resources) | ||
Preceded by Problem 35 |
Followed by Problem 37 | |
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