Q. Two circles with equal radii are intersecting at the points $(0, 1)$ and $(0, -1)$. The tangent at the point $(0, 1)$ to one of the circles passes through the centre of the other circle. Then the distance between the centres of these circles is :
Solution:
In $\Delta APO$
$\left(\frac{\sqrt{2}r}{2}\right)^{2} + 1^{2} =r^{2} $
$ \Rightarrow r= \sqrt{2} $
So distance between centres $ = \sqrt{2} r = 2 $
