Question

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:

• A. $2\sqrt{2}$
• B. $1$
• C. $2$
• D. $\sqrt{2}$

Answer 1

The correct option is C $2$


Let $C$ and $C^{\prime }$ be the centres of two circles.
$A{C}^{\prime }$ is tangent.
$\therefore \angle CA{C}^{\prime }={90}^{\circ }$
$AM=1$
$\angle CAM=\angle C^{\prime }AM={45}^{\circ }$
$\therefore CM=C^{\prime }M=1$
Distance between centres is $2$ unit.