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AI_A and (S,SB) intersect at X, Y. prove that BCX = ACY

Source: STEMS 2024, CAT A, P3

December 17, 2023
geometry

Problem Statement

Let ABCABC be a triangle. Let II be the Incenter of ABCABC and SS be the midpoint of arc BACBAC. Define IAIA as the AA-excenter wrt ABCABC. Define ω\omega to be the circle centred at SS with radius SBSB. Let AIA∩ω=XAI_A \cap \omega = X, YY. Show that ∠BCX=∠ACY\angle BCX = \angle ACY.
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