JEE Main & Advanced
JEE Main Paper (Held On 11-Jan-2019 Morning)
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\[\Delta APO,{{\left( \frac{r}{\sqrt{2}} \right)}^{2}}+{{1}^{2}}={{r}^{2}}\Rightarrow r=\sqrt{2}\] \[\therefore \]\[AB=\sqrt{2}\times \sqrt{2}=2\]