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  • In Figure, AB and CD are common tangents to two circles of unequal radii.In above question, if radii of the two circles are equal, prove that AB = CD.

In Figure, AB and CD are common tangents to two circles of unequal radii.

In the above question, if the radii of the two circles are equal, prove that AB = CD.

Answers (1)

To Prove AB = CD
According to question

It is given that the radius of both circles is equal
Hence, OA = OC = PB = PD
Here,   \angle A= \angle B= \angle C= \angle D= 90^{\circ} 
(\because tangent at any point is perpendicular to the radius at the point of contact)
Hence ABCD is a rectangle.
Opposite sides of a rectangle are equal.

\therefore AB= CD
Hence Proved.

Posted by

infoexpert27

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