MathDB
RMM 2019 Problem 2

Source: RMM 2019

February 23, 2019
RMMRMM 2019geometryComplex GeometryInversion

Problem Statement

Let ABCDABCD be an isosceles trapezoid with AB∥CDAB\parallel CD. Let EE be the midpoint of ACAC. Denote by ω\omega and Ω\Omega the circumcircles of the triangles ABEABE and CDECDE, respectively. Let PP be the crossing point of the tangent to ω\omega at AA with the tangent to Ω\Omega at DD. Prove that PEPE is tangent to Ω\Omega.
Jakob Jurij Snoj, Slovenia
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