how can I determine if 3 points can make a circle or form a circle?

Question

given three points, how can I determine if they lie on the same circle? I just want to determine if they can form a circle or not.

for example, do P(2,1), Q(0,5) and R(-1,3) lie on the same circle??

thx all!

Even then, one might consider it a degenerate circle with infinite radius. — amd, Oct 28 '17 at 18:53

score 1 · Accepted Answer · answered Oct 28 '17 at 17:26

If the $3$ points form a triangle then the circumscribed circle passes through all of them.

Thus you have to check for the degenerated case where the points are aligned, a condition could be $\vec{PQ}\wedge\vec{PR}=\vec 0$

score 0 · Answer 2 · answered Oct 28 '17 at 17:20

0

solve the System $$(2-x_M)^2+(1-y_M)^2=R^2$$ $$(0-x_M)^2+(5-y_M)^2=R^2$$ $$(-1-x_M)^2+(3-y_M)^2=R^2$$

answered Oct 28 '17 at 17:20

2 Answers2