MathDB

The triangle

ABC

is given. Let

A', B'

and

C'

be the midpoints of the sides

BC, CA

and

AB

and

O_a,O_b

and

O_c

be the circumcenters of the triangles

CAC', ABA'

and

BCB'

respectively. Prove that the triangles

ABC

and

O_aO_bO_c

are similar.
Proposed by Don Luu (Vietnam)

M2678