MathDB
Equal lengths in isosceles configuration

Source: Iberoamerican 2018 Problem 2

September 26, 2018
geometrycircumcircle

Problem Statement

Let ABCABC be a triangle such that ∠BAC=90∘\angle BAC = 90^{\circ} and AB=ACAB = AC. Let MM be the midpoint of BCBC. A point D≠AD \neq A is chosen on the semicircle with diameter BCBC that contains AA. The circumcircle of triangle DAMDAM cuts lines DBDB and DCDC at EE and FF respectively. Show that BE=CFBE = CF.
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