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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