MathDB

AK + KM = BL + LM wanted, AB = CK = CL given, perp. bisectors related

Source: Czech-Polish-Slovak Junior Match 2016, individual p4 CPSJ

January 20, 2020

geometryequal segmentsperpendicular bisector

Problem Statement

We are given an acute-angled triangle

ABC

with

AB < AC < BC

. Points

K

and

L

are chosen on segments

AC

and

BC

, respectively, so that

AB = CK = CL

. Perpendicular bisectors of segments

AK

and

BL

intersect the line

AB

at points

P

and

Q

, respectively. Segments

KP

and

LQ

intersect at point

M

. Prove that

AK + KM = BL + LM

.
Poland