Answer to Question #237 in Geometry for ken moore

Question #237

N ≥ 3 points lie on a plane, but not all of them lie on a straight line. Prove that there is a circle passing through three of these points and containing none of the remaining points.

Expert's answer

Let A and B be those of these points, the distance between which is the minimal. Then inside the circle with diameter AB there are no given points. Let C be that one of the remaining points from which the segment AB is seen under the largest angle. Then inside the circle passing through points A, B and C there are no given points.

Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

Place free inquiry

Calculate the price