Mathematics - Circle Question with Solution | TestHub

The centre of the circle is $\mathrm{C}(1,1)$ and radius of the circle is 2 , perpendicular distance from $\mathrm{C}$ on $\mathrm{AB}$, the chord $\mathrm{x}+\mathrm{y}=3$ $\begin{array}{rl}& \mathrm{CD}=\left|\frac{1+1-3}{\sqrt{2}}\right|=\frac{1}{\sqrt{2}}\\ & \Rightarrow \mathrm{AD}=\sqrt{4-\frac{1}{2}}=\sqrt{\frac{7}{2}}\left[\mathrm{AD}=\sqrt{{\mathrm{AC}}^2-{\mathrm{CD}}^2}\right]\end{array}$ Hence, the length of the chord $\mathrm{AB}=2\mathrm{AD}=2\sqrt{\frac{7}{2}}=\sqrt{14}$.