MathDB
Problems
Contests
National and Regional Contests
Taiwan Contests
TST Round 2
2019 Taiwan TST Round 2
6
6
Part of
2019 Taiwan TST Round 2
Problems
(1)
Line Passes Through Orthocenters is Parallel to BC
Source: 2019 Taiwan TST Round 2
4/1/2020
Given a triangle
△
A
B
C
\triangle{ABC}
△
A
BC
whose incenter is
I
I
I
and
A
A
A
-excenter is
J
J
J
.
A
′
A'
A
′
is point so that
A
A
′
AA'
A
A
′
is a diameter of
⊙
(
△
A
B
C
)
\odot\left(\triangle{ABC}\right)
⊙
(
△
A
BC
)
. Define
H
1
,
H
2
H_{1}, H_{2}
H
1
,
H
2
to be the orthocenters of
△
B
I
A
′
\triangle{BIA'}
△
B
I
A
′
and
△
C
J
A
′
\triangle{CJA'}
△
C
J
A
′
. Show that
H
1
H
2
∥
B
C
H_{1}H_{2} \parallel BC
H
1
H
2
∥
BC
geometry
incenter