MathDB

Let

ABC

be an acute scalene triangle and let

\omega

be its Euler circle. The tangent

t_A

\omega

at the foot of the height

A

of the triangle ABC, intersects the circle of diameter

AB

at the point

K_A

for the second time. The line determined by the feet of the heights

A

and

C

of the triangle

ABC

intersects the lines

AK_A

and

BK_A

at the points

L_A

and

M_A

, respectively, and the lines

t_A

and

CM_A

intersect at the point

N_A

.
Points

K_B, L_B, M_B, N_B

and

K_C, L_C, M_C, N_C

are defined similarly for

(B, C, A)

and

(C, A, B)

respectively. Show that the lines

L_AN_A, L_BN_B,

and

L_CN_C

are concurrent.

Problem Statement