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Prove that XY passes through a fixed point

Source: IMOC 2021 G4

August 11, 2021
geometryincenterFixed point

Problem Statement

Let DD be a point on the side ACAC of a triangle ABCABC. Suppose that the incircle of triangle BCDBCD intersects BDBD and CDCD at XX, YY, respectively. Show that XYXY passes through a fixed point when DD is moving on the side ACAC.
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