MathDB

Let

w

be the circumcircle of non-isosceles acute triangle

ABC

. Tangent lines to

w

A

and

B

intersect at point

S

. Let M be the midpoint of

AB

, and

H

be the orthocenter of triangle

ABC

. The line

HA

intersects lines

CM

and

CS

at points

M_a

and

S_a

, respectively. The points

M_b

and

S_b

are defined analogously. Prove that

M_aS_b

and

M_bS_a

are the altitudes of triangle

M_aM_bH

Problem Statement