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A = (2,2), B = (2,5) and C = (5,2) form a triangle. The circumcentre of ΔABC is

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(3,3)

(2,2)

(3.5,3.5)

(2.5,2.5)

answer is C.

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Detailed Solution

A= (2,2), B= (2,5) and C= (5,2)
Let (a,b) be the radius of the circle.
OA = OB

\Rightarrow {OA}^{2} = {OB}^{2}

\Rightarrow {(a - 2)}^{2} + {(b - 2)}^{2} = {(a - 2)}^{2} + {(b - 5)}^{2}

\Rightarrow b - 2 = \pm (b - 5)

\Rightarrow b = 3.5

OB = OC

\Rightarrow {OB}^{2} = {OC}^{2}

\Rightarrow {(a - 2)}^{2} + {(b - 5)}^{2} = {(a - 5)}^{2} + {(b - 2)}^{2}

\Rightarrow a = b = 3.5

Thus, the circumcenter of a triangle is (3.5,3.5).
So, Option 3 is correct.

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