2006 Cyprus MO/Lyceum/Problem 19
Problem
In the figure, is an isosceles triangle with and . If is an altitude of the triangle and the sector belongs to the circle , the area of the shaded region is
Solution
is a right triangle with an angle of , so it is a triangle with .
The area of the entire circle is . The central angle of the sector is , so the area is .
The area of the entire triangle is . Thus, the answer is .
See also
2006 Cyprus MO, Lyceum (Problems) | ||
Preceded by Problem 18 |
Followed by Problem 20 | |
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