This is a very simple generalisation of the well known theorem that the angle at the centre of a circle is twice the angle at the circumference subtended on the same arc. First, as is usually done, take C at the centre of the circle, fix the arc RS and take P and Q to be any points on the circumference. Then the triangles CPR and CQS must be congruent and isosceles because CP, CQ, CR and CS are radii. Hence, the angles RPS and RQS are equal and the angle at the centre RCS is equal to twice the angle at the circumference.

Now generalise this theorem to one about the angle RCS where C is any point inside the circle. The triangles are no longer isosceles, nor are they congruent to each other any more, but what can you say about them? What can you say about the angle RCS?