Question

prove that there is one and only one circle passing through three non-colinear points.

Answer 1

Theorem: There is one and only one circle passing through three given non-collinear points.

Given: Three non collinear points P, Q and R



To prove: There is one and only one circle passing through the points P, Q and R.

Construction: Join PQ and QR.

Draw perpendicular bisectors AB of PQ and CD of QR. Let the perpendicular bisectors intersect at the point O.

Now join OP, OQ and OR.