Prove that a point equidistant from 3 pointd on acircle is centre of circle
Answers
The set of points that are equidistant from two points A,B is a straight line, right? Precisely, the line that goes through the midpoint of the segment AB and is perpendicular to it. Let's call this line l(A,B).
Given 3 non-collinear points A,B,C, the lines l(A,B) and l(A,C) are not parallel, because the lines AB, AC are not parallel, and therefore meet in exactly one point. This point is equidistant from A,B,C, and is therefore the only such point. It is the center of the unique circle that goes through these three points.
Answer:
The set of points that are equidistant from two points A,B is a straight line, right? Precisely, the line that goes through the midpoint of the segment AB and is perpendicular to it. Let's call this line l(A,B).
Given 3 non-collinear points A,B,C, the lines l(A,B) and l(A,C) are not parallel, because the lines AB, AC are not parallel, and therefore meet in exactly one point. This point is equidistant from A,B,C, and is therefore the only such point. It is the center of the unique circle that goes through these three points.
Step-by-step explanation: