MathDB
A well-known geo configuration revisited

Source: Dutch TST 2024, 2.1

June 28, 2024
geometrygeometry proposedcircumcircletangent

Problem Statement

Let ABCABC be a triangle with orthocenter HH and circumcircle Γ\Gamma. Let DD be the reflection of AA in BB and let EE the reflection of AA in CC. Let MM be the midpoint of segment DEDE. Show that the tangent to Γ\Gamma in AA is perpendicular to HMHM.
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