MathDB

2

Part of 2009 Korea Junior Math Olympiad

Problems(1)

concurrent lines constructed by reflections

Source: KJMO 2009 p2

5/2/2019
In an acute triangle △ABC\triangle ABC, let A′,B′,C′A',B',C' be the reflection of A,B,CA,B,C with respect to BC,CA,ABBC,CA,AB. Let D=B′C∩BC′D = B'C \cap BC', E=CA′∩C′AE = CA' \cap C'A, F=A′B∩AB′F = A'B \cap AB'. Prove that AD,BE,CFAD,BE,CF are concurrent
geometryconcurrencyconcurrentsymmetryReflectionsgeometric transformationreflection