MathDB

$OD.OE.OF\geq 8R^3$

Source: 6-th Taiwanese Mathematical Olympiad 1997

January 18, 2007

geometrycircumcircletrigonometrygeometric transformationreflectionincenterinequalities

Problem Statement

Let

O

be the circumcenter and

R

be the circumradius of an acute triangle

ABC

. Let

AO

meet the circumcircle of

OBC

again at

D

BO

meet the circumcircle of

OCA

again at

E

, and

CO

meet the circumcircle of

OAB

again at

F

. Show that

OD.OE.OF\geq 8R^{3}