geometry - How to determine whether a point (X,Y) is contained within an arc section of a circle (i.e. a Pie slice)?

Question

Imagine a circle. Imagine a pie. Imagine trying to return a bool that determines whether the provided parameters of X, Y are contained within one of those pie pieces.

What I know about the arc:

I have the CenterX, CenterY, Radius, StartingAngle, EndingAngle, StartingPoint (point on circumference), EndingPoint (point on circumference).

Given a coordinate of X,Y, I'd like to determine if this coordinate is contained anywhere within the pie slide.

Answer 1

Check:

1. The angle from the centerX,centerY through X,Y should be between start&endangle.
2. The distance from centerX,centerY to X,Y should be less then the Radius

And you'll have your answer.