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an easy geometry from iran tst

Source: Iranian TST 2018, third exam day 1, problem 1

April 18, 2018
geometryIranIranian TST

Problem Statement

Two circles ω1(O)\omega_1(O) and ω2\omega_2 intersect each other at A,BA,B ,and OO lies on ω2\omega_2. Let SS be a point on ABAB such that OS⊥ABOS\perp AB. Line OSOS intersects ω2\omega_2  at PP (other than OO). The bisector of ASP^\hat{ASP} intersects  ω1\omega_1 at LL (AA and LL are on the same side of the line OPOP). Let KK be a point on ω2\omega_2 such that PS=PKPS=PK (AA and KK are on the same side of the line OPOP). Prove that SL=KLSL=KL.
Proposed by Ali Zamani
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