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Kyiv City MO
Kyiv City MO - geometry
Kyiv City MO Juniors 2003+ geometry
2014.9.3
2014.9.3
Part of
Kyiv City MO Juniors 2003+ geometry
Problems
(1)
2 circles internally tangent to third one (2014 Kyiv City MO 9.3)
Source:
8/6/2020
Two circles
c
1
,
c
2
{{c} _ {1}}, \, \, {{c} _ {2}}
c
1
,
c
2
pass through the center
O
O
O
of the circle
c
c
c
and touch it internally in points
A
A
A
and
B
B
B
, respectively. Prove that the line
A
B
AB
A
B
passes though a common point of circles
c
1
,
c
2
{{c} _ {1}}, \, \, {{c} _ {2}}
c
1
,
c
2
.
geometry
circles
tangent circles