MathDB

Let

C

be a circle centered at point

O

, and let

P

be a point in the interior of

C

. Let

Q

be a point on the circumference of

C

such that

PQ \perp OP

, and let

D

be the circle with diameter

PQ

. Consider a circle tangent to

C

whose circumference passes through point

P

. Let the curve

\Gamma

be the locus of the centers of all such circles. If the area enclosed by

\Gamma

1/100

the area of

C

, then what is the ratio of the area of

C

to the area of

D

Problem Statement