You are given a variable point C inside a circle and any two chords PCS and QCR through C. Investigate the angle RCS. State and prove a generalisation of the theorem about the angle at the centre of a circle being twice the angle at the circumference subtended on the same arc.

You can use the dynamic geometry applet to move the points C, P, Q, R and S and observe the changing angles.

To experiment further with this problem, download a copy of Geometer's Sketch Pad, install it, and then download and open these sketch files:

• circleAngles.gsp