MathDB

angle equality in a scalene triangle

Source: Polish Junior Olympiad 2021 Final Round Problem 4, https://omj.edu.pl

March 21, 2021

geometryangle bisector

Problem Statement

On side

AB

of a scalene triangle

ABC

there are points

M

N

such that

AN=AC

and

BM=BC

. The line parallel to

BC

through

M

and the line parallel to

AC

through

N

intersect at

S

. Prove that

\measuredangle{CSM} = \measuredangle{CSN}