MathDB

Geometric inequality again

Source: Saint Petersburg MO 2020 Grade 11 Problem 5

May 7, 2020

geometric inequalityinequalities

Problem Statement

The altitudes

BB_1

and

CC_1

of the acute triangle

\triangle ABC

intersect at

H

. The circle centered at

O_b

passes through points

A,C_1

, and the midpoint of

BH

. The circle centered at

O_c

passes through

A,B_1

and the midpoint of

CH

. Prove that

B_1 O_b +C_1O_c > \frac{BC}{4}