MathDB

perpendicular wanted when 2 triangles have same areas, circle related

Source: Czech-Polish-Slovak Junior Match 2014, Team p4 CPSJ

March 23, 2020

area of a trianglegeometryperpendicularcircleareasequal areas

Problem Statement

Point

M

is the midpoint of the side

AB

of an acute triangle

ABC

. Circle with center

M

passing through point

C

, intersects lines

AC ,BC

for the second time at points

P,Q

respectively. Point

R

lies on segment

AB

such that the triangles

APR

and

BQR

have equal areas. Prove that lines

PQ

and

CR

are perpendicular.