- The circle \(C\), with centre \(A\), passes through the point \(P\) with coordinates ( \(- 9,8\) ) and the point \(Q\) with coordinates \(( 15 , - 10 )\).
Given that \(P Q\) is a diameter of the circle \(C\),
- find the coordinates of \(A\),
- find an equation for \(C\).
A point \(R\) also lies on the circle \(C\).
Given that the length of the chord \(P R\) is 20 units, - find the length of the shortest distance from \(A\) to the chord \(P R\).
Give your answer as a surd in its simplest form.
- Find the size of the angle \(A R Q\), giving your answer to the nearest 0.1 of a degree.