Prove that if an arc of a circle subtends a right angle at any point on the remaining part of the circle, then the arc is a semi-circle.
(a) After rotating through an angle of 120 degrees through its centre of symmetry the figure looks exactly the same as its original. At what other angles will it happen for the figure? Describe with an example. (b) What is the order of rotational symmetry? (c) What is the order of rotational symmetry of a semi-circle? [4 MARKS]