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. \[5cm\].
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