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Problems
Contests
National and Regional Contests
Korea Contests
Korea Junior Mathematics Olympiad
2002 Korea Junior Math Olympiad
7
7
Part of
2002 Korea Junior Math Olympiad
Problems
(1)
2002 KJMO P7 incenter one
Source: 2002 KJMO
6/29/2024
I
I
I
is the incenter of
A
B
C
ABC
A
BC
.
D
D
D
is the intersection of
A
I
AI
A
I
and the circumcircle of
A
B
C
ABC
A
BC
, not
A
A
A
. And
P
P
P
is a midpoint of
B
I
BI
B
I
. If
C
I
=
2
A
I
CI=2AI
C
I
=
2
A
I
, show that
A
B
=
P
D
AB=PD
A
B
=
P
D
.
geometry
incenter
KJMO