MathDB

Around the acute-angled triangle

ABC

(

AC>CB

) a circle is circumscribed, and the point

N

is midpoint of the arc

ACB

of this circle. Let the points

A_1

and

B_1

be the feet of perpendiculars on the straight line

NC

, drawn from points

A

and

B

respectively (segment

NC

lies inside the segment

A_1B_1

). Altitude

A_1A_2

of triangle

A_1AC

and altitude

B_1B_2

of triangle

B_1BC

intersect at a point

K

. Prove that

\angle A_1KN=\angle B_1KM

, where

M

is midpoint of the segment

A_2B_2

Problem Statement