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0561 geometry 5th edition Round 6 p1

Source:

May 6, 2021

geometry5th edition

Problem Statement

Let

ABC

be a triangle and let

C

be a circle that intersects the sides

BC, CA

and

AB

in the points

A_1, A_2, B_1, B_2

and

C_1, C_2

respectively. Prove that if

AA_1, BB_1

and

CC_1

are concurrent lines then

AA_2, BB_2

and

CC_2

are also concurrent lines.

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