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Weirdly placed

Source: Sharygin 2019 Finals Day 1 Grade 8 P2

July 30, 2019

geometrySharygin Geometry Olympiad

Problem Statement

A point

M

inside triangle

ABC

is such that

AM=AB/2

and

CM=BC/2

. Points

C_0

and

A_0

lying on

AB

and

CB

respectively are such that

BC_0:AC_0 = BA_0:CA_0 = 3

. Prove that the distances from

M

to

C_0

and

A_0

are equal.

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