MathDB
Floating orthocenter forms an if and only if condition

Source: 2019 Baltic Way P12

November 18, 2019
geometry

Problem Statement

Let ABCABC be a triangle and HH its orthocenter. Let DD be a point lying on the segment ACAC and let EE be the point on the line BCBC such that BC⊥DEBC\perp DE. Prove that EH⊥BDEH\perp BD if and only if BDBD bisects AEAE.
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