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 thenTB = TP.................→(ii)
From (i) and (ii) , we get:=> TA = TB