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Prove the concurrency of three lines

Source: XVII Sharygin Correspondence Round P3

March 2, 2021

geometry

Problem Statement

Altitudes

AA_1,CC_1

of acute-angles

B_0A_1 , B_0C_1

meet at point

H

;

B_0

is the midpoint of

AC

. A line passing through

B

and parallel to

AC

meets

B_0A_1 , B_0C_1

at points

A',C'

respectively. Prove that

AA',CC'

and

BH

concur.

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