CAT Exam Model Paper 4 with solutions for free online practice

Let the co-ordinates of A and B be (0,0) and (a,0) respectively.
Let the co-ordinates of point C be (h, k).
Given:
2AC = BC
⇒$2\sqrt{{\mathit{h}}^2+{\mathit{k}}^2}=\sqrt{{\left(\mathit{h}-\mathit{a}\right)}^2+{\mathit{k}}^2}$
$\Rightarrow 4\left({\mathit{h}}^2+{\mathit{k}}^2\right)={\left(\mathit{h}-\mathit{a}\right)}^2+{\mathit{k}}^2$
⇒$4{\mathit{h}}^2+4{\mathit{k}}^2={\mathit{h}}^2+{\mathit{k}}^2+{\mathit{a}}^2-2\mathit{a}\mathit{h}$
$\Rightarrow {\mathit{h}}^2+{\mathit{k}}^2+\frac{2\mathit{a}}{3}\mathit{h}-\frac{{\mathit{a}}^2}{3}=0$
$\Rightarrow {\left(\mathit{h}+\frac{\mathit{a}}{3}\right)}^2+{\mathit{k}}^2=\mathrm{}{\left(\frac{2\mathit{a}}{3}\right)}^2$
The equation written above is that of a circle with center (say O) at $\left(-\frac{\mathit{a}}{3},0\right)$ and radius $\frac{2\mathit{a}}{3}$The center O $\left(-\frac{\mathit{a}}{3},0\right)$ divides AB externally suchthat 4AO = BO.