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In figure, AB and CD are common tangents...

In figure, AB and CD are common tangents to two circles of unequal radii. Prove that AB=CD

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Given AB and CD are common tangent to two circles of unequal radius
To prove AB=CD

Construction Produce AB and CD, to intersect at P.
Proof PA=PC
[the length of tangents drawn from an internal point to a circle are equal]
Also, PB=PD
[the lengths of tangents drawn from an internal point to a circle are equal]
`:.PA-PB=PC-PD`
AB=CD Hence proved.
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