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Kvant 2022
M2702
M2702
Part of
Kvant 2022
Problems
(1)
Incenter-excenter geo
Source: All-Russian 2022 9.2
4/19/2022
Given is triangle
A
B
C
ABC
A
BC
with incenter
I
I
I
and
A
A
A
-excenter
J
J
J
. Circle
ω
b
\omega_b
ω
b
centered at point
O
b
O_b
O
b
passes through point
B
B
B
and is tangent to line
C
I
CI
C
I
at point
I
I
I
. Circle
ω
c
\omega_c
ω
c
with center
O
c
O_c
O
c
passes through point
C
C
C
and touches line
B
I
BI
B
I
at point
I
I
I
. Let
O
b
O
c
O_bO_c
O
b
O
c
and
I
J
IJ
I
J
intersect at point
K
K
K
. Find the ratio
I
K
/
K
J
IK/KJ
I
K
/
K
J
.
geometry