Question

if two circle touch Each Other externally the centre and the point of contact are collinear prove​

Answer 1

By adding the points P,O,S and also the points Q,O; ans R,O.

From the given condition , ∠POQ=90°

=∠ROS. [since, the angle as described like semi-circle is a right angle.]

Now,from the figure we see ∠POR=180°−90°=∠QOS. And hence,∠POQ+∠QOS=90°+90°=180°=∠POS.

Hence ,we can conclude P,O,S are collinear.

However, that the distance between the two centres will be equal to the difference between the two radii is because the centres and the contact point are colinear