MathDB

incenter of PA_0Q lies on altitude of ABC

Source: 2022 Saudi Arabia JBMO TST 2.3

November 1, 2022

geometryincenter

Problem Statement

Let

BB_1

and

CC_1

be the altitudes of acute-angled triangle

ABC

, and

A_0

is the midpoint of

BC

. Lines

A_0B_1

and

A_0C_1

meet the line passing through

A

and parallel to

BC

at points

P

and

Q

. Prove that the incenter of triangle

PA_0Q

lies on the altitude of triangle

ABC

.

Back to Problems View on AoPS