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The answer is 1.
Here is the theorem:
There is a unique circle passing through points P1 , P2 , P3 if and only if these three points are non-collinear.
The proof is not too hard, but involves some linear algebra. I will post a link to it.
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How many planes can be drawn through any three noncollinear points in a plane?
just one
How many lines can be drawn through three noncollinear points?
If you are talking about straight lines, the answer is NONE, because that is what noncollinear means. If curves are allowed, then the answer is infinitely many.
Are three noncollinear points always contained in only one plane?
Yes a plane can always be drawn three any three points, whether they are linear or not.
What does three noncollinear points determine?
A plane
The number of noncollinear points needed to determine a circle?
Three.
How many planes can be drawn through any three noncollinear points in a plane?
just one
How many lines can be drawn through three noncollinear points?
If you are talking about straight lines, the answer is NONE, because that is what noncollinear means. If curves are allowed, then the answer is infinitely many.
Are three noncollinear points always contained in only one plane?
Yes a plane can always be drawn three any three points, whether they are linear or not.
How many planes can be drawn through any three noncollinear points?
Only one plane can pass through 3 non-collinear points.
What does three noncollinear points determine?
A plane
How many noncollinear points are needed to define a plane?
Three.
The number of noncollinear points needed to determine a circle?
Three.
What is a triangle defined as?
The shape identified by three noncollinear points.
Can three points be noncoplanar?
No, A plane can be drawn through any 3 points. If the 3 points are collinear then they make a line and a plane can contain a line. If the points are noncollinear then they can be used to form the corners of a triangle; all points of a triangle are in the same plane.
Can one plane sometimes pass through three noncollinear points?
no
The number of noncollinear points needed to determine a unique plane?
Three
A triangle is a figure formed by three segments connecting three noncollinear points?
fal;se
