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Isogonal conjugates!

Source:

February 4, 2015
geometrycircumcirclerhombusangle bisector

Problem Statement

Let ABCABC be an acute-angled triangle with circumcircle ω\omega , and let OO , HH be the triangle's circumcenter and orthocenter respectively . Let also A′A^{'} be the point where the angle bisector of the angle BACBAC meets ω\omega . If A′H=AHA^{'}H=AH , then find the measure of the angle BACBAC.
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