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<OAH = <LSA wanted, circumcenter, orthocenter, midpoint, perp. bisector

Source: 2nd SAFEST Olympiad 2020 p4 - South AFrica + ESTonia TST

October 4, 2020
geometryequal anglesCircumcenterorthocenter

Problem Statement

Let OO be the circumcenter and HH the orthocenter of an acute-triangle ABCABC. The perpendicular bisector of AOAO intersects the line BCBC at point SS. Let LL be the midpoint of OHOH. Prove that ∠OAH=∠LSA\angle OAH = \angle LSA.
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