Question

The point of intersection of the perpendicular bisectors of the sides of a triangle is called.

1) Circumcentre
2) Incentre
3) Congruent
4) Concurrent

Answer 1

Hint: We have to find out the name of the point of intersection of the perpendicular bisectors of the sides of a triangle. The perpendicular bisector refers to the line that intersects the other line at the right angle and divides it into two equal parts. Apply the definitions of given options to find the correct answer.

Complete solution step by step:
The perpendicular is the line from the vertex that makes an angle of ${90^ \circ }$ with the base.
As we know, the triangle has three sides and there will be three perpendiculars, one from each vertex.
In this question, we are asked about perpendicular bisectors of the triangle, that is the line which intersects the side of the triangle at ${90^ \circ }$ and passing through the midpoint.
We know that the perpendicular bisector divides the side of the triangle into 2 equal parts.
But, if the lines would not have been perpendicular and only bisectors, then the lines are known as medians and the point of intersection of medians is known as the centroid.
Also, if the angle bisectors meet at a point, the point of intersection of angle bisectors is known as incentre.
Therefore, the point of intersection of the perpendicular bisectors of the sides of a triangle is called circumcentre.
Hence, option A is the correct answer.

Note: There is one more way in which we can define the circumcentre. The centre of a circle which is drawn outside a triangle is known as circumcentre. And similarly, the centre of a circle which is drawn inside a triangle is known as an incentre. Circumcentre and incentre are the same in the case of an equilateral triangle.