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Angle between Line PQ and BC

Source: 2008 Japan Mathematical Olympiad Finals Problem 3

February 12, 2008
geometrycircumcirclegeometry proposed

Problem Statement

Given an acute-angled triangle ABC ABC with circumcenter O. O. The circle passing through two points A, O A,\ O intersects with the line AB AB and AC AC at P, Q P,\ Q other than A A respectively. If the lengths of the line segments PQ, BC PQ,\ BC are equal, then find the angle ≤90∘ \leq 90^\circ that the lines PQ PQ and BC BC make.
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