MathDB

Points

A

B

and

C

lie on one side of the angle with the vertex at point

O

, and points

A'

B'

and

C'

lie on the other. It is known that

B

is the midpoint of the segment

AC

B'

is the midpoint of the segment

A'C'

, and lines

AA'

BB'

and

CC'

are parallel (fig.). Prove that the centers of the circles circumscribed around the triangles

OAC

OA'C

and

OBB'

lie on the same straight line. https://cdn.artofproblemsolving.com/attachments/d/6/92831077781bc45f25e9f71077034f84753a59.png

8.5