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a triangle with altitudes

Source: Bulgarian NMO 2017, 3rd round, p.6

April 22, 2017

geometry

Problem Statement

An acute non-isosceles

\triangle ABC

is given.

CD, AE, BF

are its altitudes. The points

E', F'

are symetrical of

DC_1=3CD

with respect accordingly to

A

and

B

. The point

C_1

lies on

\overrightarrow{CD}

, such that

DC_1=3CD

. Prove that

\angle E'C_1F'=\angle ACB

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