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Tournament Of Towns
1996 Tournament Of Towns
(489) 2
(489) 2
Part of
1996 Tournament Of Towns
Problems
(1)
ext. common tangent to 2 non-intersecting circles
Source: TOT 489 1996 Spring J A2 Tournament Of Towns
8/16/2024
An exterior common tangent to two non-intersecting circles with centers and
O
2
O_2
O
2
touches them at the points
A
1
A_1
A
1
and
A
2
A_2
A
2
respectively. The segment
O
1
O
2
O_1O_2
O
1
O
2
intersects the circles at the points
B
1
B_1
B
1
and
B
2
B_2
B
2
respectively.
C
C
C
is the point where the straight lines
A
1
B
1
A_1B_1
A
1
B
1
and
A
2
B
2
A_2B_2
A
2
B
2
meet.
D
D
D
is the point on the line
A
1
A
2
A_1A_2
A
1
A
2
such that
C
D
CD
C
D
is perpendicular to
B
1
B
2
B_1B_2
B
1
B
2
. Prove that
A
1
D
=
D
A
2
A_1D = DA_2
A
1
D
=
D
A
2
.
geometry
common tangent