We have
Then,
O and O′be the centre of two circles.
XY be a common tangent.
P is the mid point of OandO′.
Construct:-draw OX and OX′.
Then,
InΔOPXandO′PX
OP=O′P(radiusofcircle)
PX=PX(Commonline)
∠XPO=∠XPO′(Every90o)
Then,
ΔOPX≅ΔO′PX
So, OPO′ are collinear.