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Problem 5 of Finals

Source: IX International Festival of Young Mathematicians Sozopol, Theme for 10-12 grade

September 22, 2018

geometrygeometry unsolved

Problem Statement

On the extension of the heights

AH_1

and

BH_2

of an acute

\triangle ABC

, after points

H_1

and

H_2

, are chosen points

M

and

N

in such way that

\angle MCB = \angle NCA = 30^\circ

.
We denote with

C_1

the intersection point of the lines

MB

and

NA

. Analogously we define

A_1

and

B_1

. Prove that the straight lines

AA_1

,

BB_1

, and

CC_1

intersect in one point.

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