Mock AIME 4 2006-2007 Problems/Problem 4
Problem
Points , , and are on the circumference of a unit circle so that the measure of is , the measure of is , and the measure of is . The area of the triangular shape bounded by and line segments and can be written in the form , where and are relatively prime positive integers. Find .
Solution
Let the center of the circle be . The area of the desired region is easily seen to be that of sector plus the area of triangle minus the area of triangle . Using the area formula to compute the areas of the two triangles, this is , so the answer is .
See also
Mock AIME 4 2006-2007 (Problems, Source) | ||
Preceded by Problem 3 |
Followed by Problem 5 | |
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