Question

AB and CD are common tangents to two circles of equal radii. Prove that AB=CD.

Answer 1

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.