MathDB

KP is parallel to median

Source: European Mathematical Cup, 2015, Senior, P3

December 30, 2016

geometrycirclesmedian

Problem Statement

Circles

k_1

and

k_2

intersect in points

A

and

B

, such that

k_1

passes through the center

O

of the circle

k_2

. The line

p

intersects

k_1

in points

K

and

O

and

k_2

in points

L

and

M

, such that the point

L

is between

K

and

O

. The point

P

is orthogonal projection of the point

L

to the line

AB

. Prove that the line

KP

is parallel to the

M-

median of the triangle

ABM

.
Matko Ljulj

Back to Problems View on AoPS