Given three points in the plane is it always possible to fin

Given three points in the plane, is it always possible to find a fourth point in the plane that is the same distance from each of the three points?

Solution

Hi,

I think the following helps you to better understanding.

There will be two cases arise.

Case-1) let the given three points are non - collinear. Then they form a triangle. So its circumcentre will be the required point,which is equidistant from all the three given points( here vertices of triangle)

We are clear with the following procedure to find that circumcenter.

I) draw perpendicular bisectors of all three sides of the triangle

ii) then the point of intersection of all three perpendicular bisectors will be the circumcentre ,which is our required one.

Case-2)

If the given three points are non collinear then we cannot find the fourth point which is equidistant to the given three other points.

I hope you like this