I have been doing some STEP past papers for fun and I stumbled on a problem that is giving me trouble. The question is linked here 
I am completely stuck as I don't have an idea how to approach the first part. I drew the diagram and I recognized the cyclic quadrilateral inside the circle, however, I am not sure how to use the perpendicular bisectors of the chords. I know that a perpendicular bisector to a chord has a direction towards the centre but I don't know how this could be used to solve the problem. If anybody could suggest an intuitive way of thinking about it and using the information given in the question I would be really thankful.
The 2 chords are perpendicular if and only if their perpendicular bisectors are also perpendicular.
It's much easier to deal with their perpendicular bisectors esp since you know that they intersect at the center (which is the origin), then it is to find the intersection of $LM$ and $PQ$.
What is the equation for the perpendicular bisectors (or at least, the directional vector)?
What does it mean for these 2 lines to be perpendicular?