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Q.

The angle between two tangents drawn from an external point P  to a circle of radius a   and centre O   is 60 °  then the length of OP   will be ____.


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Detailed Solution

The angle between two tangents drawn from an external point P  to a circle of radius a   and centre O   is 60 °  then the length of OP   will be 2a  .
Given that the angle between the tangents is 60 °   .
Naming the points of contact as Q   and R  .
Question ImageUsing the theorem, tangents drawn from an external point to a circle are equidistant and at equal angles.
We get,
PQ=PR ∠OPR=∠OPQ   ∠OPQ= ∠QPR 2 ∠OPQ= 30 °   [Given ∠QPR= 60 °  ]
Considering the ΔOPQ  ,
sin 30 ° =  Perpendicular   Hypotenuse  1 2 = a OP OP =2a  
Thus the length of  OP =2a  .
 
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The angle between two tangents drawn from an external point P  to a circle of radius a   and centre O   is 60 °  then the length of OP   will be ____.