MathDB
equal segments wanted, symmetric point , <A=60 given

Source: II Brazilian Olympic Revenge 2003 p3

April 22, 2020
geometrySymmetricequal segments

Problem Statement

Let ABCABC be a triangle with ∠BAC=60∘\angle BAC =60^\circ. A′A' is the symmetric point of AA wrt BC‾\overline{BC}. DD is the point in AC‾\overline{AC} such that AB‾=AD‾\overline{AB}=\overline{AD}. HH is the orthocenter of triangle ABCABC. ll is the external angle bisector of ∠BAC\angle BAC. {M}=A′D‾∩l\{M\}=\overline{A'D}\cap l,{N}=CH‾∩l\{N\}=\overline{CH} \cap l. Show that AM‾=AN‾\overline{AM}=\overline{AN}.
Back to ProblemsView on AoPS