Let $\overline{AB}$ be a diameter of a circle, and let $C$ be a point on the circle such that $AC = 4$ and $BC = 4.$ The angle bisector of $\angle ACB$ intersects the circle at point $M.$ Find $CM.$
\({\color{blue}\overline{CM}}=\overline{AB}=\sqrt{4^2+4^2}=\sqrt{32}\color{blue}=5.65685\)
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+1032 
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