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National and Regional Contests
Russia Contests
Adygea Teachers' Geometry Olympiad
2021 Adygea Teachers' Geometry Olympiad
1
1
Part of
2021 Adygea Teachers' Geometry Olympiad
Problems
(1)
tangent segment of 2 circles (2021 Adygea Teachers' Geometry Olympiad p1)
Source:
3/31/2021
a) Two circles of radii
6
6
6
and
24
24
24
are tangent externally. Line
ℓ
\ell
ℓ
touches the first circle at point
A
A
A
, and the second at point
B
B
B
. Find
A
B
AB
A
B
. b) The distance between the centers
O
1
O_1
O
1
and
O
2
O_2
O
2
of circles of radii
6
6
6
and
24
24
24
is
36
36
36
. Line
ℓ
\ell
ℓ
touches the first circle at point
A
A
A
, and the second at point
B
B
B
and intersects
O
1
O
2
O_1O_2
O
1
O
2
. Find
A
B
AB
A
B
.
geometry
tangent