Answer the following with solutions:

Question

A secant and a tangent segment intersect at the exterior of a circle. The chord which is a part of the secant is three times as long as the tangent and the external segment of the secant is 12 cm. find the length of the tangent segment.

Answer 1

The theorem you need is this:

If from a point without a circle a tangent and secant are drawn, the tangent is a mean proportional between the whole segment and its external segment.