One And Only One Circle Can Pass Through Three Non-col-linear Points Theorem-1 Mathematics Metric Grade-10

Diagram

Given: A, B and C are three non-col-linear point in a plane.
To Prove: One and only one circle can pass through three non col-linear points A, B and C.
CONSTRUCTION:  Join A with B and B with C.  Drawn DF ⊥ bisector to AB and HK  | bisector to BC. 
So, DF and HK are not parallel and they intersect each other at point O. Also join A, B and C with point O.



Proof:

Every Point on DF is equidistant from A and B.          DF ⊥ bisector to AB
In particular mOA = mOB                   ....(i)
Similarly every point on HK  is equidistant from        HK ⊥ bisector to BC
B and C.
In particular  mOB = mOC                  ...(ii)
Now O is the only point common to DF and  HK 

which is equidistant from A, B and C.  

i.e mOA = mOB = mOC                                                   by  (i) and (ii)

So, there is no such point except O.

ONE AND ONLY ONE CIRCLE CAN PASS THROUGH

THREE NON-COL-LINEAR POINTS. METRIC GRADE-10