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  • Write ‘True’ or ‘False’ and justify your answer in each of the following : If angle between two tangents drawn from a point P to a circle of radius a and centre O is 60°, then OP=a sqroot 3

Write ‘True’ or ‘False’ and justify your answer in each of the following: If the angle between two tangents drawn from a point P to a circle of radius a and centre O is 60^{\circ}, then. OP= a\sqrt{3}

Answers (1)

Given \angle APB= 60^{\circ} 
Draw line OP from point O to P which bisects P. Which bisect \angle P
i.e, \angle APO= 30^{\circ}
In \bigtriangleup OAP
\sin 30^{\circ}= \frac{OA}{OP}
\therefore \sin \theta = \frac{perpendicular}{hypotenuse}
 
\frac{1}{2}= \frac{a}{OP}
OP = 2a

Hence the value of OP = 2a
Hence the given statement is False.

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infoexpert27

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