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Izogonal points

Source: Romanian 2018 TST Day 2 Problem 1

May 25, 2020
geometryMiquel pointSymedian

Problem Statement

Let ABCABC be a triangle, and let MM be a point on the side (AC)(AC) .The line through MM and parallel to BCBC crosses ABAB at NN. Segments BMBM and CNCN cross at PP, and the circles BNPBNP and CMPCMP cross again at QQ. Show that angles BAPBAP and CAQCAQ are equal.
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