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angle chasing from Cono Sur, isosceles, circumcircle, equal angles wanted

Source: Cono Sur Shortlist 2003 G1

July 26, 2019
geometrycircumcircleequal anglesAngle Chase

Problem Statement

Let OO be the circumcenter of the isosceles triangle ABCABC (AB=ACAB = AC). Let PP be a point of the segment AOAO and QQ the symmetric of PP with respect to the midpoint of ABAB. If OQOQ cuts ABAB at KK and the circle that passes through A,KA, K and OO cuts ACAC in LL, show that ∠ALP=∠CLO\angle ALP = \angle CLO.
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