MathDB
Shortlist 2017/G4

Source: Shortlist 2017, Romanian TST 2018

July 10, 2018
geometryIMO Shortlistgeometry solvedhomothetytangent circlespower of a pointexcircle

Problem Statement

In triangle ABCABC, let ω\omega be the excircle opposite to AA. Let D,ED, E and FF be the points where ω\omega is tangent to BC,CABC, CA, and ABAB, respectively. The circle AEFAEF intersects line BCBC at PP and QQ. Let MM be the midpoint of ADAD. Prove that the circle MPQMPQ is tangent to ω\omega.
Back to ProblemsView on AoPS