Prove that an angle subtended by an arc is double at the centre then at the perimeter.

After drawing, bisect the perimeter angle in two from the centre. We now have two isosceles triangles with the sides the same length (1 radius from the centre). We know that 2 angles in each triangle add up to A, lets call these angles C and D. 

From the diagram (shown on whiteboard) We have two angles E and F at the centre of the circle. E is equal to (180 - 2C) and F is equal to (180 - 2 D). As angles in a circle add up to 360 we know B is equal to 360 - (180 - 2C) - (180 -2D) = 2C + 2D = 2(C + D) = 2A.

Hence we have B is double the size of A as required.

Optional Extra: Use this to prove that angles formed in a circle from the same two points on circumference have the same angle between them.