MathDB

M2750

Part of Kvant 2023

Problems(1)

Two triangles have equal areas

Source: Kvant Magazine No. 6 2023 M2750

1/9/2024
Let D,ED, E and FF{} be the midpoints of the sides BC,CABC, CA and ABAB{} of the acute-angled triangle ABCABC and let Ha,HbH_a, H_b and HcH_c{} be the orthocenters of the triangles ABD,BCEABD, BCE and CAFCAF{} respectively. Prove that the triangles HaHbHcH_aH_bH_c and DEFDEF have equal areas.
Proposed by Tran Quang Hung
geometryareas