1960 AHSME Problems/Problem 7
Problem
Circle passes through the center of, and is tangent to, circle . The area of circle is square inches. Then the area of circle , in square inches, is:
Solutions
Solution 1
Since Circle is tangent to circle and touches the center of circle , the diameter of circle is the radius of circle .
That means circle is twice as big as circle , so the area of circle is four times as big as circle .
The area of circle is square inches, so the answer is .
Solution 2
Since Circle is tangent to circle and touches the center of circle , the diameter of circle is the radius of circle .
Applying the area formula , substitute for to solve for the radius of circle .
That means the diameter of circle (or the radius of circle ) is . Apply the area formula again to find the area of circle .
The answer is .
See Also
1960 AHSC (Problems • Answer Key • Resources) | ||
Preceded by Problem 6 |
Followed by Problem 8 | |
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