O is the incenter of a triangle ABC. A circle of
center O cuts AB, BC, and AC (extended if necessary) at D, E, F, G, H, and
M, as shown in the figure below. Prove that (1) the triangle EAH is isosceles (AE = AH),
similarly, the triangles DBF and GCM are isosceles; (2) DE = FG = HM.

#Euclidean #Geometry Problem 1340 #Triangle #Incenter #Concentric Circles, #Isosceles Triangles, #Congruence https://t.co/7wrHFni1ep pic.twitter.com/FlCmY2riDJ

— Antonio Gutierrez (@gogeometry) August 9, 2017

— José Luis da Vila (@jldavilaa01) August 10, 2017

1 Incenter + 1 Circle Concentric w/Incenter = 😮? (T/Y 2 @gogeometry) https://t.co/QTTT3e8VgI @geogebra #math #mathchat #mathGIF #mathchat pic.twitter.com/ilPJjWMZXR

— Tim Brzezinski (@dynamic_math) August 15, 2017