1976 AHSME Problems/Problem 24
Problem
In the adjoining figure, circle has diameter ; circle is tangent to circle and to at the center of circle ; and circle tangent to circle , to circle and . The ratio of the area of circle to the area of circle is
Solution
Let and be the radius of and the radius of respectively. It follows that the radius of is
Suppose is the foot of the perpendicular from to We construct the auxiliary lines, as shown below: In right we have and By the Pythagorean Theorem, we get
In right we have and By the Pythagorean Theorem, we get
We equate the expressions for then simplify: Therefore, the ratio of the area of to the area of is
~MRENTHUSIASM
See Also
1976 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 23 |
Followed by Problem 25 | |
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