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Argentina MO 2021 National Level 2 P2

Source:

April 23, 2022
geometrycontests

Problem Statement

In a semicircle with center OO, let CC be a point on the diameter ABAB different from A,BA, B and O.O. Draw through CC two rays such that the angles that these rays form with the diameter ABAB are equal and that they intersect at the semicircle at DD and at EE. The line perpendicular to CDCD through DD intersects the semicircle at K.K. Prove that if D≠E,D\neq E, then KEKE is parallel to AB.AB.
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