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equilateral wanted, <C=60^o, altitudes and midpoint

Source: 2006 Bosnia & Herzegovina JBMO TST p2

May 27, 2020

geometryEquilateralaltitude

Problem Statement

In an acute triangle

ABC

\angle C = 60^o

. If

AA'

and

BB'

are two of the altitudes and

C_1

is the midpoint of

AB

, prove that triangle

C_1A'B'

is equilateral.