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

 


Solution

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

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