Find the center and diameter of the circle below?

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Answer 1 · 2016-08-26T17:39:58

See the Explanation.

We take any $3$ $3$ distinct points, say, $A, B and C$ $A, B and C$ on the circle.

Draw the $⊥$ $bot$ -bisectors, say, $l_{1} and l_{2}$ $l_1 and l_2$ of line-segments

$A B, and, B C$ $AB, and, BC$ .

Since, the pts. $A, B, C$ $A, B, C$ are non-colliner , $l_{1} \cap l_{2} \neq ϕ$ $l_1nnl_2!=phi$ .

Let $l_{1} \cap l_{2} = {P}$ $l_1nnl_2={P}$ , then $P$ $P$ is the Centre of the circle passing thro.

$A, B, C$ $A,B,C$ .

A Diameter $A D$ $AD$ of this circle can be obtained by joining $A$ $A$ with the

centre $P$ $P$ , and, extending the line-segment $A P$ $AP$ so as to meet

the circle in pt. $D \neq A$ $D!=A$ .