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  • If the angle between two tangents drawn from an external point P to a circle of radius a and centre O, is  , then find the length of OP.

If the angle between two tangents drawn from an external point P to a circle of radius a and centre O, is  60^{\circ}, then find the length of OP.

 

 

 

 
 
 
 
 

Answers (1)

Given : Circle with radius = a

\angle QP\!R = 60^{\circ}

To find : OP

We know that the line joining the point of bisector of tangents (P) and center of circle (O) bisects the angle b/w tangents (\angle QP\!R )

\Rightarrow \angle QP\!R =\frac{60^{\circ}}{2}=30^{\circ}

Now in  \bigtriangleup PQO, [\angle Q=90^{\circ}]

\sin 30 = \frac{OQ}{OP} = \frac{a}{OP}

\Rightarrow \frac{1}{2} = \frac{a}{OP} \Rightarrow OP=2a

Posted by

Ravindra Pindel

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