question_answer

Two circles with equal radii are intersecting at the points (0, 1) and (\[0,\text{ }-1\]). 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 circle is [JEE Main Online Paper (Held On 11-Jan-2019 Morning]

A) \[2\sqrt{2}\]                              

B)               1     

C)               \[\sqrt{2}\]                                            

D)               2

Correct Answer: D

Solution :

Now, let r be the equal radii of both the circles. APB is a right angled triangle.            \[\therefore \]\[AB=\sqrt{2}r\] Also,\[AO=OB=\frac{r}{\sqrt{2}}\] In\[\Delta APO,{{\left( \frac{r}{\sqrt{2}} \right)}^{2}}+{{1}^{2}}={{r}^{2}}\Rightarrow r=\sqrt{2}\] \[\therefore \]\[AB=\sqrt{2}\times \sqrt{2}=2\]