MathDB

12

Part of 2020 Baltic Way

Problems(1)

Midpoints of arcs and a bunch of right angles

Source: Baltic Way 2020, Problem 12

11/14/2020
Let ABCABC be a triangle with circumcircle ω\omega. The internal angle bisectors of ∠ABC\angle ABC and ∠ACB\angle ACB intersect ω\omega at X≠BX\neq B and Y≠CY\neq C, respectively. Let KK be a point on CXCX such that ∠KAC=90∘\angle KAC = 90^\circ. Similarly, let LL be a point on BYBY such that ∠LAB=90∘\angle LAB = 90^\circ. Let SS be the midpoint of arc CABCAB of ω\omega. Prove that SK=SLSK=SL.
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