The Angle in a Semicircle Theorem states that the angle subtended by a diameter of a circle at the circumference is a right angle. An alternative statement of the theorem is the angle inscribed in a semicircle is a right angle. Proof Draw a radius of the circle from C. This makes two isosceles triangles.
The circumference of a circle is π x diameter so the length of a semicircle is (1/2)π x d. The solution to problem #2 is shown below. Let the diameters of the smaller circles be p, q, r, s. Use the formula to find the lengths of each semicircle. The same thinking is applicable to semicircle