Two circles touch each other externally at point P. Q is a point on the common tangent through P. Prove that the tangents QA and QB are equal.

Solution:

Suppose,

   

be the point from which,

   

are two tangents with centre

   

So,

   

Similarly, from point

   

are two tangents with centre

   

So,

   

From

   

we have

   

So, tangents

   

are equal.

– Hence Proved