SOLUTION: How many circles are determined by nine points?

Question 936245: How many circles are determined by nine points?
Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
Your question is too vague. For any three points in the plane, not all collinear, there is a unique circle that passes through those points, in which the number of circles is at most 9C3 = 84, assuming no two circles are the same. Or you could be referring to the famous nine-point circle of a triangle, which is determined by the midpoints of the sides, the feet of the altitudes, and the midpoints of the lines from the sides to the orthocenter.
RELATED QUESTIONS
question:How many lines are determined by 8 points, no 3 of which are collinear? how many (answered by tutorvolunteer)

how many planes are determined by 9 points no three of which are collinear? (answered by Edwin McCravy)

how many planes are determined by 7 points,no three of which are collinear (answered by jim_thompson5910)

How many triangles are determined by (answered by richwmiller)

GIVEN 4 noncoplanar points, no three of which are collinear. How many planes are... (answered by jim_thompson5910)

How many triangles are determined by 20 points in a plane, no three of which are... (answered by richwmiller)

How many triangles are determined by 20 points if no three of them are in a... (answered by richard1234)

How many lines are determined by n points, no three of which are collinear? Thank you (answered by robertb)

how many lines are determined by the given condition? 1.Five coplanar points, no three... (answered by ikleyn)