Question

In Fig. 9.13, AB and CD are common tangents to two circles of unequal radii. Prove that AB = CD.

Answer 1

simple!
just draw another tangent AD
now consider tangents AD & DC.
since,
length of tangent from an external point to a circle is equal
AD=CD()
AD=AB(same reason)
from() & ()
AB=CD
hence proved

Answer 2

Just draw another tangent AD.

Now consider tangents AD & DC.

Since lenghts of tangents from an external point to a circle is equal,

                 AD = CD  ---------[1]

Similarly, AD = AB   ---------[2]    ( with the same reason) .

Now from [1] & [2]

                  AB = CD

                                 Hence proved.

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