MathDB

Let

\overline{AB}

be a line segment of length 2,

C_1

be the circle with diameter

\overline{AB}

C_0

be the circle with radius 2 externally tangent to

C_1

A

, and

C_2

be the circle with radius 3 externally tangent to

C_1

B

. Duck

D_1

is located at point

B

, Duck

D_2

is located on

C_2

, 270 degrees counterclockwise from

B

, and Duck

D_0

is located on

C_0

, 270 degrees counterclockwise from

A

. At the same time, the ducks all start running counterclockwise around their corresponding circles, with each duck taking the same amount of time to complete a full lap around its circle. When the 3 ducks are first collinear, the distance between

D_0

and

D_2

can be expressed as

p\sqrt{q}

. Find

p+q

.
2022 CCA Math Bonanza Individual Round #10

Problem Statement