Question

If two circles touch each other externally, prove that the centres and the point of contact are collinear.

Answer 1

The figure shows 2 circles which touch each other externally. We have drawn a tangent through that point which is common to both the circles, thus being tangent to both the circles.

We know that a tangent makes an angle of 90 degrees with the line joining the center with the point of tangency.

So, In circle 1,

The Green Angle $=90$ degrees

In circle 2,

The Red angle $=90$ degrees.

So the angle b/w both the lines joining the center with the point of tangency make an angle of 90+90=180 degrees.

That is, the points of contact and the centers are collinear.