MathDB
Problems
Contests
National and Regional Contests
Taiwan Contests
TST Round 1
2019 Taiwan TST Round 1
6
6
Part of
2019 Taiwan TST Round 1
Problems
(1)
Mathematical Reflections
Source: 2019 Taiwan TST Round 1
3/31/2020
Given a triangle
△
A
B
C
\triangle ABC
△
A
BC
. Denote its incenter and orthocenter by
I
,
H
I, H
I
,
H
, respectively. If there is a point
K
K
K
with
A
H
+
A
K
=
B
H
+
B
K
=
C
H
+
C
K
AH+AK = BH+BK = CH+CK
A
H
+
A
K
=
B
H
+
B
K
=
C
H
+
C
K
Show that
H
,
I
,
K
H, I, K
H
,
I
,
K
are collinear.Proposed by Evan Chen
geometry proposed
geometry