1. Tardigrade
  2. Question
  3. Mathematics
  4. From a point P(3,3) on the circle x2+y2=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 )

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. 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 $R$ )

NTA AbhyasNTA Abhyas 2020Conic Sections

Solution:

Solution
$QM^{2}=QP^{2}-PM^{2}=OQ^{2}-OM^{2}$
$\Rightarrow 4-x^{2}=18-\left(3 \sqrt{2} - x\right)^{2}$ (where, $PM=x$ )
$\Rightarrow 6\sqrt{2}x=4\Rightarrow x=\frac{\sqrt{2}}{3}$ units