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2023 RMM, Problem 4

Source: 2023 RMM, Problem 4

March 4, 2023

geometryRMM 2023inequalitiesGeometry inequality

Problem Statement

An acute triangle

ABC

is given and

H

and

O

be its orthocenter and circumcenter respectively. Let

K

be the midpoint of

AH

and

\ell

be a line through

O.

Let

P

and

Q

be the projections of

B

and

C

\ell.

Prove that

KP+KQ\ge BC