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Circumcenter, incentre and Simson-Wallace line

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March 4, 2021
geometryincentercircumcircle

Problem Statement

Let OO be the circumcenter of triangle ABC,ABC, and DD be an arbitrary point on the circumcircle of ABC.ABC. Let points X,YX, Y and ZZ be the orthogonal projections of point DD onto lines OA,OBOA, OB and OC,OC, respectively. Prove that the incenter of triangle XYZXYZ is on the Simson-Wallace line of triangle ABCABC corresponding to point D.D.
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