# Circular triangle

Geometry Level pending

$$\Gamma$$ is a semicircle with $$A$$ and $$B$$ as endpoints of the diameter and $$O$$ as the center. $$C$$ is a point on $$\Gamma$$ such that $$\angle AOC = 162^\circ$$ and $$D$$ is the midpoint of $$\stackrel{\frown}{AC}$$. If the radius of $$\Gamma$$ is $$10$$ and the area of the region bounded by $$\stackrel{\frown}{BC}$$, $$CD$$ and $$DB$$ can be expressed as $$M \pi$$, what is the value of $$M$$?

Details and assumptions

All line segments are straight, unless otherwise denoted by the arc symbol e.g. $$\stackrel{\frown} {AC}$$.

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