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.

To solve the two problems below you need to know 1) The area of a circle is Πr2, with r as radius and that the area of a semicircle is of course half of the circle, ½Πr2 and 2) the angle in a semicircle theorem. Problem 1 Prove that the area of the solid green semicircle

Two roads connect Towns A and B. One passes through Town C which lies between A and B and the other a direct route. The roads are semicircular. Which road will you take if you want to conserve on gas? Why? Try this problem with your Facebook friends. It’s not that hard. Tricky, maybe. Like