MathDB
2021 Geo #4: Trapezoidzzzz

Source:

May 30, 2021
geometry

Problem Statement

Let ABCD be a trapezoid with AB∥CD,AB=5,BC=9,CD=10,AB \parallel CD, AB = 5, BC = 9, CD = 10, and DA=7DA = 7. Lines BCBC and DADA intersect at point EE. Let MM be the midpoint of CDCD, and let NN be the intersection of the circumcircles of △BMC\triangle BMC and △DMA\triangle DMA (other than MM). If EN2=abEN^2 = \tfrac ab for relatively prime positive integers aa and bb, compute 100a+b100a + b.
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