Question

Question 5
In figure AB and CD are common tangents to two circles of unequal radii prove that AB=CD

Answer 1

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

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]
$\Rightarrow$ PA – PB = PC – PD
$\Rightarrow$ AB = CD
Hence proved.