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Question

A pair of perpendicular tangents are drawn to a circle from an external point. Prove that length of each tangent is equal to the radius of the circle.

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Solution

It is given that a pair of perpendicular tangents are drawn to the circle that means APB=900 as shown in the above figure:

Therefore,

PA=PB (Tangents from the external point P)

PAO=PBO=900 (Radius and tangents are perpendicular)

OA=OB (Radii of same circle)

Thus, AOBP is a square.

Now we have AP=PB=OA=OB

Hence, the length of tangent is equal to radii of the circle.




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