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239 Open Math Olympiad
2015 239 Open Mathematical Olympiad
1
A Geometry About Gergonne Triangle
A Geometry About Gergonne Triangle
Source: 239 2015 P1
May 14, 2020
geometry
Problem Statement
Let the incircle of triangle
A
B
C
ABC
A
BC
touches the sides
A
B
,
B
C
,
C
A
AB,BC,CA
A
B
,
BC
,
C
A
in
C
1
,
A
1
,
B
1
C_1,A_1,B_1
C
1
,
A
1
,
B
1
respectively. If
A
1
C
1
A_1C_1
A
1
C
1
cuts the parallel to
B
C
BC
BC
from
A
A
A
at
K
K
K
prove that
∠
K
B
1
A
1
=
90.
\angle KB_1A_1=90.
∠
K
B
1
A
1
=
90.
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