¶ 2017 AMC 10B Problem 22
Problem:
The diameter of a circle of radius is extended to a point outside the circle so that . Point is chosen so that and line is perpendicular to line . Segment intersects the circle at a point between and . What is the area of ?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Because is inscribed in a semicircle, it is a right angle. Therefore is similar to , so their areas are related as is to . Because and, by the Pythagorean Theorem,
this ratio is . The area of is , so the area of is .
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The problems on this page are the property of the MAA's American Mathematics Competitions