MathDB

Given is an acute triangle

ABC

and the points

A_1,B_1,C_1

, that are the feet of its altitudes from

A,B,C

respectively. A circle passes through

A_1

and

B_1

and touches the smaller arc

AB

of the circumcircle of

ABC

in point

C_2

. Points

A_2

and

B_2

are defined analogously. Prove that the lines

A_1A_2

B_1B_2

C_1C_2

have a common point, which lies on the Euler line of

ABC

1.1