Question

If two circles touch each other externally or internally, the point of contact lies on the line joining their centres.Prove it.

Answer 1

The answer is in the pic.

Hope it helps you!

Answer 2

Given : two circles touch each other,

To Find : prove that their point of contact lies on the line joining their centers.​

Solution:

Two circles touches each other at  A

Center are x  and y  of each circle

Draw a tangent PA    ( P is a point out side circle )

Hence ∠XAP = 90°  and ∠ YAP = 90°

∠XAP  + ∠ YAP = 90°  + 90°

=>∠XAP  + ∠ YAP = 180°

Hence XPY is a straight line

so  point of contact lies on the line joining their centers.​

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