Question

AB and CD are common tangents to two circles of unequal radii.prove that AB=CD​

Answer 1

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Answer 2

AB = CD, as the tangents drawn from the external point to circle are equal.

Centre of two circles = O1  and O2. (Given)

Let AB and CD be the common tangents to the circles that intersect in P.

AP = PC --- eq 1  ( As length of the tangents drawn from an external point to the circle are always equal)

PB = PD ) --- eq 2  ( As length of the tangents drawn from an external point to the circle are always equal)  

Adding the equations (1) and (2),

Therefore,

= AP + PB = PC + PD

= AB = CD