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