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triangle construction related to touchpoints of incircle with triangle sides

Source: Sharygin 2010 Final 9.4

October 6, 2018

geometryconstructionincircle

Problem Statement

In triangle

ABC

, touching points

A', B'

of the incircle with

BC, AC

and common point

G

of segments

AA'

and

BB'

were marked. After this the triangle was erased. Restore it by the ruler and the compass.