Question

The length of the chord $x + y = 3$ intercepted by the circle $x^2 + y^2 - 2x - 2y - 2 = 0$ is

• A. $\frac{7}{2}$
• B. $\frac{3\sqrt{3}}{2}$
• C. $\sqrt{14}$
• D. $\frac{\sqrt{17}}{2}$

Answer 1

Answer: (C)

$\sqrt{14}$

Answer 2

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