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CK + KM = BL + LM if AK = AL = BC

Source: 2022 Saudi Arabia November Camp Test 2.2 BMO + EGMO TST

November 1, 2022

geometryequal segments

Problem Statement

Given is an acute triangle

ABC

with

BC < CA < AB

. Points

K

and

L

lie on segments

AC

and

AB

and satisfy

AK = AL = BC

. Perpendicular bisectors of segments

CK

and

BL

intersect line

BC

at points

P

and

Q

, respectively. Segments

KP

and

LQ

intersect at

M

. Prove that

CK + KM = BL + LM