Given : Circles C1 and C2 of radii r1 and r2 respectively and r1<r2.
AB and CD are two common tangents.
To prove : AB=CD
Construction : Produce AB and CD upto P where both tangents meet.
Proof : Tangents from an external point to a circle are equal.
For circle C1,PB=PD __(i)
and the circle C2,PA=PC __(ii)
Subtracting (i) from (ii), we have
PA−PB=PC−PD
⇒AB=CD
Hence, proved.