Question

What will be the locus of three non collinear points A,B and C?Justify your answer.​

Answer 1

Answer:

The locus of a point equidistant from three non-collinear points A, B and C is the circumcentre of the triangle.

The locus of the points is the point of intersection of the perpendicular bisectors of each of the two points. The circumcentre is equidistant from all the three points A, B and C.

Example:

Answer 2

See when we talk about locus then we have little idea about locus that is a locus is a equidistant from all point for example if i am talkong about a circle so for circle the locus point is its circle because that centre define the all property and describe all geometry view and circumference of circle is equidistant that why centre is locus for circle

Now, three non colinear point the first geometry which come in mind that is triangle so basically it is talking about triangle locus that why triangle locus is intersection of median/ perpediculars of triangle is locus either we say circumcentre, centroid, incircle or orthocentre all arr depends upon triangle which you explain in it. But by default its equilateral thats why locus is circumcentre or incircle or orthocentre or centroid is locus of three non colinear points.