MathDB

Line Passes Through Orthocenters is Parallel to BC

Source: 2019 Taiwan TST Round 2

April 1, 2020

geometryincenter

Problem Statement

Given a triangle

\triangle{ABC}

whose incenter is

I

and

A

-excenter is

J

A'

is point so that

AA'

is a diameter of

\odot\left(\triangle{ABC}\right)

. Define

H_{1}, H_{2}

to be the orthocenters of

\triangle{BIA'}

and

\triangle{CJA'}

. Show that

H_{1}H_{2} \parallel BC