ΒΆ 1994 AHSME Problem 17
Problem:
An by rectangle has the same center as a circle of radius . The area of the region common to both the rectangle and the circle is
Answer Choices:
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Solution:
Let be the center of the circle and rectangle, and let the circle and rectangle intersect at and as shown. Since and , the width of the rectangle, it follows that . Hence . The sum of the areas of sectors and is . The sum of the areas of isosceles right triangles and is . Thus, the area of the region common to both the rectangle and the circle is .
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