question_answer

In Fig. 3, AP and BP are tangents to a circle with centre O, such that \[AP=5\text{ }cm\] and \[\angle APB=60{}^\circ \]. Find the length of chord AB.

Answer:

Given, AP and BP are tangents to a circle with centre O.

\[\therefore \,\,~AP=BP\]

Now, \[\angle APB=60{}^\circ \] (Given)

\[\therefore \,\,~\angle PAB=\angle PBA=60{}^\circ \]                             \[(~\because AP=BP)\]

Thus, \[\Delta \text{ }APB\] is an equilateral triangle.

Hence, the length of chord AB is equal to the length of AP i.e. \[5cm\].