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Bosnia and Herzegovina TST 2003 Day 2 Problem 1

Source: Bosnia and Herzegovina Team Selection Test 2003

September 18, 2018
geometryisoscelesorthogonalaltitudesAngle Chasing

Problem Statement

In triangle ABCABC ADAD and BEBE are altitudes. Let LL be a point on EDED such that EDED is orthogonal to BLBL. If LB2=LDā‹…LELB^2=LD\cdot LE prove that triangle ABCABC is isosceles
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