Question

From a point $P\left(3,3\right)$ on the circle $x^2+y^2=18$ two chords $PQ$ and $PR$ each of length $2$ units are drawn on this circle. Then, the value of the length $PM$ is equal to (where, $M$ is the midpoint of the line segment joining $Q$ and $R$ )

• A. $\frac{1}{3\sqrt{2}}$ units
• B. $\frac{1}{2}$ units
• C. $\frac{\sqrt{2}}{3}$ units
• D. $\frac{4}{9}$ units

Answer 1

Answer: (C)

$Q{M}^2=Q{P}^2-P{M}^2=O{Q}^2-O{M}^2$
$\Rightarrow 4-x^2=18-{\left(3\sqrt{2}-x\right)}^2$ (where, $PM=x$ )
$\Rightarrow 6\sqrt{2}x=4\Rightarrow x=\frac{\sqrt{2}}{3}$ units