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VTRMC
2010 VTRMC
Problem 5
Problem 5
Part of
2010 VTRMC
Problems
(1)
circle internally tangent to another
Source: VTRMC 2010 P5
5/17/2021
Let
A
,
B
A,B
A
,
B
be two circles in the plane with
B
B
B
inside
A
A
A
. Assume that
A
A
A
has radius
3
3
3
,
B
B
B
has radius
1
1
1
,
P
P
P
is a point on
A
A
A
,
Q
Q
Q
is a point on
B
B
B
, and
A
A
A
and
B
B
B
touch so that
P
P
P
and
Q
Q
Q
are the same point. Suppose that
A
A
A
is kept fixed and
B
B
B
is rolled once round the inside of
A
A
A
so that
Q
Q
Q
traces out a curve starting and finishing at
P
P
P
. What is the area enclosed by this curve? https://services.artofproblemsolving.com/download.php?id=YXR0YWNobWVudHMvOS84LzkwMDBjOTAwODk5M2QyM2IxMGUxZGE5OTI1NWU1ZDYwMDkyYTUwLnBuZw==&rn=VlRSTUMgMjAxMC5wbmc=
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