MathDB

Let

ABC

be an acute triangle with circumcenter

O

and circumradius

R

AO

meets the circumcircle of

BOC

A'

BO

meets the circumcircle of

COA

B'

and

CO

meets the circumcircle of

AOB

C'

. Prove that

OA'\cdot OB'\cdot OC'\geq 8R^{3}.

Sorry if this has been posted before since this is a very classical problem, but I failed to find it with the search-function.

Problem Statement