MathDB

Let

A,B

be two circles in the plane with

B

inside

A

. Assume that

A

has radius

3

B

has radius

1

P

is a point on

A

Q

is a point on

B

, and

A

and

B

touch so that

P

and

Q

are the same point. Suppose that

A

is kept fixed and

B

is rolled once round the inside of

A

so that

Q

traces out a curve starting and finishing at

P

. What is the area enclosed by this curve? https://services.artofproblemsolving.com/download.php?id=YXR0YWNobWVudHMvOS84LzkwMDBjOTAwODk5M2QyM2IxMGUxZGE5OTI1NWU1ZDYwMDkyYTUwLnBuZw==&rn=VlRSTUMgMjAxMC5wbmc=

Problem Statement