Circle 3 points

Construct any 3 points A,B,C

Join  AB and BC and draw perpendiculars from mid-points P,Q of AB,BC which intersect at O.

Join AO and BO

     AP = BP       (construct)

     OP = OP       (common)

   ^APO = ^BPO     (construct)

So  tri.APO = tri.BPO  (2 sides and inc.angle equal)

So AO = BO

Similarly CO = BO

So AO = BO = CO are radii of circle centered at O.

Created 24th July 2008