1. The semi-circle and the inscribed circle have a common tangent in E. The radius of a circle is perpendicular to the tangent in the tangent point. Since OE is a radius and CE is a radius OE and CE must be the same line. Thus the three points are collinear.

2. To find the radius of the inscribed circle draw the tangent at the semi-circle in E. The tangent crosses the line AB in F. Draw the angle bisector of . The angle bisector cuts OE in C. CE is the radius in question.

3. There is at least one property missing to prove that . This construction actually asks you to construct a symmetric kite.