The problem calls for simple geometrical reasoning (nothing more complicated than similar triangles) and leads to an obvious generalisation. Finding the solution is the beginning of the next stage:
how can I explain my method?
is this the best method?
what if...can I generalise this result?
Key questions
What do you know about the tangent to a circle and its radius?
What do you know about the perpendicular from the centre of a circle to a chord?
Can you spot any similar triangles?
If two sides of a right-angled triangle are in the ratio 3:5 what can we say about the third side?