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Kürschák Math Competition
1997 Kurschak Competition
2
2
Part of
1997 Kurschak Competition
Problems
(1)
O, I and orthocenter of intouch triangle collinear
Source: Kürschák 1997, problem 2
7/15/2014
The center of the circumcircle of
△
A
B
C
\triangle ABC
△
A
BC
is
O
O
O
. The incenter of the triangle is
I
I
I
, and the intouch triangle is
A
1
B
1
C
1
A_1B_1C_1
A
1
B
1
C
1
. Let
H
1
H_1
H
1
be the orthocenter of
△
A
1
B
1
C
1
\triangle A_1B_1C_1
△
A
1
B
1
C
1
. Prove that
O
O
O
,
I
I
I
, and
H
1
H_1
H
1
are collinear.
geometry
circumcircle
incenter
geometry unsolved