2020 CIME I Problems/Problem 5
Let be a rectangle with sides and let be the reflection of over . If and the area of is , find the area of .
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Let be the center of rectangle . Because is the reflection of over and degrees, we have degrees. This means lies on the circle with diameter , or the circumcircle of rectangle . We are given , so by symmetry, . Since the three lengths are equal and degrees, we must have degrees, so , , are all equilateral. Given that the area of cyclic quadrilateral is , the area of is . This is of the area of rectangle , so the answer is .
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