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International Contests
Tournament Of Towns
1994 Tournament Of Towns
(416) 4
(416) 4
Part of
1994 Tournament Of Towns
Problems
(1)
fixed length for AK, common ext. tangent of incircles of ABD, ACD
Source: TOT 416 1994 Spring A S4 - Tournament of Towns
6/12/2024
A point
D
D
D
is placed on the side
B
C
BC
BC
of the triangle
A
B
C
ABC
A
BC
. Circles are inscribed in the triangles
A
B
D
ABD
A
B
D
and
A
C
D
ACD
A
C
D
, their common exterior tangent line (other than
B
C
BC
BC
) intersects
A
D
AD
A
D
at the point
K
K
K
. Prove that the length of
A
K
AK
A
K
does not depend on the position of
D
D
D
. (An exterior tangent of two circles is one which is tangent to both circles but does not pass between them.) (I Sharygin)
geometry
fixed