MathDB
Elementary area geometry

Source: pOMA 2023/2

November 21, 2023
geometryarea of a triangleAngle Chasingcyclic quadrilateralcircumcircle

Problem Statement

Let △ABC\triangle ABC be an acute triangle, and let D,E,FD,E,F respectively be three points on sides BC,CA,ABBC,CA,AB such that AEDFAEDF is a cyclic quadrilateral. Let OBO_B and OCO_C be the circumcenters of △BDF\triangle BDF and △CDE\triangle CDE, respectively. Finally, let D′D' be a point on segment BCBC such that BD′=CDBD'=CD. Prove that △BD′OB\triangle BD'O_B and △CD′OC\triangle CD'O_C have the same surface.
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