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 .
An image is supposed to go here. You can help us out by creating one and editing it in. Thanks.
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 .
|2020 CIME I (Problems • Answer Key • Resources)|
|1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15|
|All CIME Problems and Solutions|
The problems on this page are copyrighted by the MAC's Christmas Mathematics Competitions.