Find the co-ordinates of the centre of the circle passing through the points `(0,0)`,`(-2,1)` and `(-3,2)`. Also find its radius.

Explanation

Assume, P(x, y) be the centre of the circle passing through the points `O(0,0), A(-2,1) and B(-3,2)`. So,


`OP = AP = BP`


As, `OP = AP`


`Rightarrow OP^{2}=AP^{2}`


`Rightarrow x^{2}+y^{2}=(x+2)^{2}+(y-1)^{2}`


`Rightarrow x^{2}+y^{2}=x^{2}+y^{2}+4 x-2 y+5`


`Rightarrow 4 x-2 y+5=0 cdot(1)`


As, `OP = BP`


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