MathDB
Easy Geometry

Source: Indian TST 2019 Practice Test 2 P1

July 17, 2019
geometrycircumcircleangle bisectorrectangleradical axis

Problem Statement

Let the points OO and HH be the circumcenter and orthocenter of an acute angled triangle ABC.ABC. Let DD be the midpoint of BC.BC. Let EE be the point on the angle bisector of ∠BAC\angle BAC such that AE⊥HE.AE\perp HE. Let FF be the point such that AEHFAEHF is a rectangle. Prove that D,E,FD,E,F are collinear.
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