MathDB

Two triangles have equal areas

Source: Kvant Magazine No. 6 2023 M2750

January 9, 2024

geometryareas

Problem Statement

Let

D, E

and

F{}

be the midpoints of the sides

BC, CA

and

AB{}

of the acute-angled triangle

ABC

and let

H_a, H_b

and

H_c{}

be the orthocenters of the triangles

ABD, BCE

and

CAF{}

respectively. Prove that the triangles

H_aH_bH_c

and

DEF

have equal areas.
Proposed by Tran Quang Hung

Back to Problems View on AoPS