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Find angle

Source: Sharygin Geometry Olympiad 2012 - Problem 6

April 28, 2012

symmetrygeometrycircumcircleinradiusincentertrigonometrytrapezoid

Problem Statement

Point

C_{1}

of hypothenuse

AC

of a right-angled triangle

ABC

is such that

BC = CC_{1}

. Point

C_{2}

on cathetus

AB

is such that

AC_{2} = AC_{1}

; point

A_{2}

is defined similarly. Find angle

AMC

, where

M

is the midpoint of

A_{2}C_{2}