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express angles of DEO in terms of angles of ABC, perpendicular bisectors

Source: 2014 Saudi Arabia Pre-TST 2.4

September 12, 2020
geometrycircumcircleperpendicular bisector

Problem Statement

Let ABCABC be an acute triangle with ∠A<∠B≤∠C\angle A < \angle B \le \angle C, and OO its circumcenter. The perpendicular bisector of side ABAB intersects side ACAC at DD. The perpendicular bisector of side ACAC intersects side ABAB at EE. Express the angles of triangle DEODEO in terms of the angles of triangle ABCABC.
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