2021 JMPSC Invitationals Problems/Problem 10
A point is chosen in isosceles trapezoid with , , , and . If the sum of the areas of and is , then the area of can be written as where and are relatively prime. Find
It is implied lies on the line that bisects and . We have the area of the trapezoid is since the height is . Now, subtracting we have for is the height of . This means , asserting the area of is
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