MathDB

collinear wanted, circumcircles related to an isosceles

Source: 2011 Oral Moscow Geometry Olympiad grades 8-9 p5

April 17, 2020

geometrycircumcirclecollinearisosceles

Problem Statement

Let

AA _1

and

BB_1

be the altitudes of an isosceles acute-angled triangle

ABC, M

the midpoint of

AB

. The circles circumscribed around the triangles

AMA_1

and

BMB_1

intersect the lines

AC

and

BC

at points

K

and

L

, respectively. Prove that

K, M

, and

L

lie on the same line.