The equation of the perpendicular bisectors of the sides AB and AC of a triangle ABC are $y = x$ and $y = - x + 2$ , respectively. Then, the circumcentre of a triangle is

(0, 0)

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(4, 4)

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(3, 3)

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None of these

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Solution

The correct option is D None of these
Consider the given figure. The outer circle circumscribes the triangle ABC.
Let OD and OE be the perpendicular bisectors of AB and AC.
Now we know that perpendicular drawn from the centre of a circle bisects its chords. AB, BC, AC are nothing but chords of the circle.
Hence the intersection of the perpendicular bisectors of the AB and AC will give us the circumcentre O.
It is known that $y = x$ defines OD and $y = - x + 2$ defines OE.
Solving the equations, $y = - x$ and $y = - x + 2$ , we get
$x = 1$ and $y = 1$
Hence $O = (1, 1)$ .

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