MathDB

Elementary Geometry

Source: Bulgaria National Olympiad 2020

June 30, 2020

geometry

Problem Statement

On the sides of

\triangle{ABC}

points

P,Q \in{AB}

(

P

is between

A

and

Q

) and

R\in{BC}

are chosen. The points

M

and

N

are defined as the intersection point of

AR

with the segments

CP

and

CQ

, respectively. If

BC=BQ

,

CP=AP

,

CR=CN

and

\angle{BPC}=\angle{CRA}

, prove that

MP+NQ=BR

.

Back to Problems View on AoPS