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projections of projections on altitudes result to a segment parallel to 3rd side

Source: 2012 Sharygin Geometry Olympiad Final Round 9.1

August 3, 2018

geometryaltitudes

Problem Statement

The altitudes

AA_1

and

BB_1

of an acute-angled triangle ABC meet at point

O

. Let

A_1A_2

and

B_1B_2

be the altitudes of triangles

OBA_1

and

OAB_1

respectively. Prove that

A_2B_2

is parallel to

AB

.
(L.Steingarts)