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1984 IMO Shortlist
18
18
Part of
1984 IMO Shortlist
Problems
(1)
Determine the radius of k
Source:
9/8/2010
Inside triangle
A
B
C
ABC
A
BC
there are three circles
k
1
,
k
2
,
k
3
k_1, k_2, k_3
k
1
,
k
2
,
k
3
each of which is tangent to two sides of the triangle and to its incircle
k
k
k
. The radii of
k
1
,
k
2
,
k
3
k_1, k_2, k_3
k
1
,
k
2
,
k
3
are
1
,
4
1, 4
1
,
4
, and
9
9
9
. Determine the radius of
k
.
k.
k
.
geometry
trigonometry
circles
radius
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