MathDB

JBMO TST Moldova Problem 1

Source: JBMO TST Moldova Problem 1

October 13, 2020

geometryperimeter

Problem Statement

Let there be a triangle

ABC

with orthocenter

H

. Let the lengths of the heights be

h_a, h_b, h_c

from points

A, B

and respectively

C

, and the semi-perimeter

p

of triangle

ABC

. It is known that

AH \cdot h_a + BH \cdot h_b + CH \cdot h_c = \frac{2}{3} \cdot p^2

. Show that

ABC

is equilateral.

Back to Problems View on AoPS