MathDB

The inscribed circle

\omega

of the triangle

ABC

touches its sides

BC, CA

and

AB

at points

A_1, B_1

and

C_1

, respectively. Let

S

be the intersection point of lines passing through points

B

and

C

and parallel to

A_1C_1

and

A_1B_1

respectively,

A_0

be the foot of the perpendicular drawn from point

A_1

B_1C_1

G_1

be the centroid of triangle

A_1B_1C_1

P

be the intersection point of the ray

G_1A_0

with

\omega

. Prove that points

S, A_1

, and

P

lie on a straight line.

Problem Statement