MathDB

Consider an acute triangle

ABC

in which

A_1, B_1,

and

C_1

are the feet of the altitudes from

A, B,

and

C,

respectively, and

H

is the orthocenter. The perpendiculars from

H

onto

A_1C_1

and

A_1B_1

intersect lines

AB

and

AC

P

and

Q,

respectively. Prove that the line perpendicular to

B_1C_1

that passes through

A

also contains the midpoint of the line segment

PQ

Problem Statement