MathDB
similar triangles externally to a triangle lead to a similar of circumcenters

Source: Germany Federal - Bundeswettbewerb Mathematik 2010, round 1, p3

April 10, 2020
geometrysimilar trianglesCircumcentercircumcircle

Problem Statement

On the sides of a triangle XYZXYZ to the outside construct similar triangles YDZ,EXZ,YXFYDZ, EXZ ,YXF with circumcenters K,L,MK, L ,M respectively. Here are ∠ZDY=∠ZXE=∠FXY\angle ZDY = \angle ZXE = \angle FXY and ∠YZD=∠EZX=∠YFX\angle YZD = \angle EZX = \angle YFX. Show that the triangle KLMKLM is similar to the triangles . https://cdn.artofproblemsolving.com/attachments/e/f/fe0d0d941015d32007b6c00b76b253e9b45ca5.png
Back to ProblemsView on AoPS