Question

The three perpendicular bisectors of a triangle intersect at the _______.

Question 12 options:

a)

circumcenter

b)

incenter

c)

centroid

d)

orthocenter

Answer 1

a) circumcenter

Explanation:

You want to know the name of the point of intersection of the three perpendicular bisectors of the sides of a triangle.

Circumcircle

Each side of a triangle is a chord of the circumscribed circle. The perpendicular bisector of a chord is a line through the center of the circle. Hence the point of concurrency of the perpendicular bisectors of the sides of a triangle is the center of the circumscribed circle.

The name of the center of the circle circumscribing a triangle is "circumcenter."

__

Additional comment

When the triangle is a right triangle, the circumcenter is the midpoint of the hypotenuse, which is a diameter of the circle.