How to know if a point is inside a circle?

Having a circle with the centre (xc,yc) with the radius r how to know whether a point (xp,yp) is inside the circle?

Answer

The distance between xc,yc and xp,yp is given by the Pythagorean theorem as d=(xpxc)2+(ypyc)2. The point xp,yp is inside the circle if d<r, on the circle if d=r, and outside the circle if d>r. You can save yourself a little work by comparing d2 with r2 instead: the point is inside the circle if d2<r2, on the circle if d2=r2, and outside the circle if d2>r2. Thus, you want to compare the number (xpxc)2+(ypyc)2 with r2.

Attribution
Source : Link , Question Author : Ivan , Answer Author : Brian M. Scott

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