Chapter 6, Problem 9CR

Solution

To Prove: $\overleftrightarrow{PQ}$ is perpendicular to $\overleftrightarrow{AB}$

Given information: M is the mid-point of $\overleftrightarrow{AB}$ is provided in the question which will help to find the solution.

Proof: Here, AM = MB ( $\because$ M is the mid-point of $\overleftrightarrow{AB}$ )

And, PQ is the radius of the circle which intersects the chord at its mid-point.

Hence, radius is perpendicular to chord

So, $\overleftrightarrow{PQ}\perp \overleftrightarrow{AB}$