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orthocenter wanted, tangents of circumcircle of 2 projections related

Source: Mathley 2015 p3

August 18, 2020
circumcircleorthocenterprojectionsgame strategy

Problem Statement

A point PP is interior to the triangle ABCABC such that AP⊥BCAP \perp BC. Let E,FE, F be the projections of CA,ABCA, AB. Suppose that the tangents at E,FE, F of the circumcircle of triangle AEFAEF meets at a point on BCBC. Prove that PP is the orthocenter of triangle ABCABC.
Do Thanh Son, High School of Natural Sciences, National University, Hanoi
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