MathDB

AM=KB wanted, AK =AO, KM =MC , KM //AC (2021 Kyiv City MO 8.4.1)

Source:

February 16, 2021

geometryequal segments

Problem Statement

On the sides

AB

and

BC

of the triangle

ABC

, the points

K

and

M

are chosen so that

KM \parallel AC

. The segments

AM

and

KC

intersect at the point

O

. It is known that

AK =AO

and

KM =MC

. Prove that

AM=KB