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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 90°, then

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 center O is 90^{\circ}, then OP= a\sqrt{2}

Answers (1)

Answer True
Solution
            
Given  \angle APB= 90^{\circ}
Draw line OP from point O to P which bisects \angle P .
i.e, \angle OPB= 45^{\circ}
In \bigtriangleup OBP
\sin 45= \frac{OB}{OP}
\therefore \sin \theta = \frac{perpendicular}{hypotenuse}

\frac{1}{\sqrt{2}}= \frac{a}{OP}
OP= a\sqrt{2}
Hence the given statement is True.



 

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