Geometry
# Properties of Circles

$C$ and $B$ are both externally tangent to each other and inscribed in circle $A.$ The radius of circle $A$ is $11,$ the radius of circle $B$ is $6,$ and the radius of circle $C$ is $5.$ What is the sum of the lengths of $\overline{AC}$ and $\overline{BC}?$

In the above diagram, circles**Note:** The above diagram is not drawn to scale.

$\lvert \overline{AD} \rvert,$ is $12,$ then the two circles become externally tangent to each other. If $\lvert \overline{AD} \rvert=4,$ the smaller circle becomes inscribed in the larger one. What is the radius of the larger circle?

Consider two fixed circles with different radii as shown in the above diagram. If the distance between their centers, denoted$O$ is the center of the circle and the length of $\overline{OA}$ is $4.$ What is the length of $\overline{BC}?$

In the above diagram,$14$ by removing one semicircle with radius $7$ on the left and adding one semicircle with radius $7$ on the right. What is the circumference of the symbol?

The above partial yin yang symbol is created from a large semicircle with radius