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right triangle wanted, perpendicular given , symmetric of vertex wrt midpoint

Source: 2015 Saudi Arabia GMO TST III p3

August 1, 2020
geometryright triangleperpendicularSymmetric

Problem Statement

Let ABCABC be a triangle, with AB<ACAB < AC, DD the foot of the altitude from A,MA, M the midpoint of BCBC, and B′B' the symmetric of BB with respect to DD. The perpendicular line to BCBC at B′B' intersects ACAC at point PP . Prove that if BPBP and AMAM are perpendicular then triangle ABCABC is right-angled.
Liana Topan
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