The horizontal line XY with O some way along it, the points B and A, where B is (not directly) above Y, and A is (not directly) above X. The lines OA and OB and the angles they make with XY are marked. There is a circle centre C above XY to which OA and OB are both tangent.

In the diagram, \(OA\) and \(OB\) are tangents to the circle, centre \(C\) and radius \(\quantity{4.5}{in.}\) . The lines \(OA\), \(OB\) are inclined at \(55^\circ\) and \(25^\circ\) respectively to the straight line \(XOY\).


  1. the angle \(COY\);

What does the line \(OC\) do to the angle \(AOB\)? Can you prove this? Which properties of tangents to a circle do you know?

  1. the distance of \(C\) from the line \(XOY\).

Could we draw in the line we need on our diagram? What can we say now?