Hi,

I drew a diagram with $C(0,4)$ the centre of the circle and $P(x,y)$ an arbitrary point in the plane

I drew a vertical line through $P$ and a horizontal line through $C,$ intersecting at $A.$

The point $P$ is on the circle with centre $C$ and radius 3 if and only if the distance from $P$ to $C$ is 3. What is the distance from $C$ to $A?$ What is the distance from $A$ to $P?$ What is the distance from $P$ to $C?$ What does Pythagoras theorem tell you about the triangle $PCA?$

Penny