MathDB

Given are triangle

ABC

and line

\ell

intersecting

BC, CA

and

AB

at points

A_1, B_1

and

C_1

respectively. Point

A'

is the midpoint of the segment between the projections of

A_1

AB

and

AC

. Points

B'

and

C'

are defined similarly. (a) Prove that

A', B'

and

C'

lie on some line

\ell'

. (b) Suppose

\ell

passes through the circumcenter of

\triangle ABC

. Prove that in this case

\ell'

passes through the center of its nine-points circle.
M. Marinov and N. Beluhov

Problem Statement