An equilateral triangle lies inside a circle. If we draw a perpendicular bisector of equilateral triangle and the angle bisector of two angles meet at a point in the perpendicular bisector then how it is the centre of the circle.

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Solution

The circum centre is the intersection of the perpendicular bisectors of the three sides.
Now in an equilateral triangle, the angle bisector also bisects the opposite side at right angles.
hence the intrsection f the perpendicular bisector and the angle bisector will give the centre of the circumscribed circle.

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