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<BCA=? if 2AP=BC, BX=BY, symmetrics (2021 Novosibirsk Oral Geo Oly 7.5)

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April 27, 2021
geometryanglesequal segments

Problem Statement

In an acute-angled triangle ABCABC on the side ACAC, point PP is chosen in such a way that 2AP=BC2AP = BC. Points XX and YY are symmetric to PP with respect to vertices AA and CC, respectively. It turned out that BX=BYBX = BY. Find ∠BCA\angle BCA.
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