MathDB
Circumcircle tangency

Source: Philippine MO 2022/6

March 19, 2022
geometrycircumcircle

Problem Statement

In △ABC\triangle ABC, let DD be the point on side BCBC such that AB+BD=DC+CA.AB+BD=DC+CA. The line ADAD intersects the circumcircle of △ABC\triangle ABC again at point X≠AX \neq A. Prove that one of the common tangents of the circumcircles of △BDX\triangle BDX and △CDX\triangle CDX is parallel to BCBC.
Back to ProblemsView on AoPS