Two circles touch each other externally:

Given: Two circles with respective centres C1 and C2 touch each other externaly at the point P. T is any point on the common tangent to the circles, TA and TBare two tangents drawn from the point T to the circles. 

To prove : TA = TB

Proof : TA and TP are two tangents drawn from a point T outside the circle whose centre is C1 and so they are equal in length.
∴  TA = TP --------→(I)
Similarly TB and TP are two tangents from an external point T then
TB = TP.................→(ii)

From (i) and (ii) , we get:
=> TA = TB