# 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. \( \stackrel{\frown} {AC}\).