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proof of angle bisector within an equilateral triangle

Source: May Olympiad (Olimpiada de Mayo) 1999 L2

September 12, 2018
geometryangle bisectorEquilateral Triangle

Problem Statement

Let ABCABC be an equilateral triangle. MM is the midpoint of segment ABAB and NN is the midpoint of segment BCBC. Let PP be the point outside ABCABC such that the triangle ACPACP is isosceles and right in PP. PMPM and ANAN are cut in II. Prove that CICI is the bisector of the angle MCAMCA .
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