MathDB

Another problem from Carlos Shine's notes(20th problem)

Source: https://ghoshadi.files.wordpress.com/2018/03/angle-chasing-carlos-shine-mop-2010.pdf

May 19, 2019

geometryTrianglesimilar trianglesproofs

Problem Statement

(Olympic Revenge 2008) Let

ABC

be a triangle and

M

the midpoint of

BC

. Let

D

and

E

be points such that

ABC

DBA

and

EAC

are similar (in this order). The symmedians of

D

with respect to

DBA

and

E

with respect to

EAC

meet at

K

. Suppose that AM/BC=√3/2 Prove that

KAB

and

KCA

are similar (in this order).