Question

Which of the following is correct regarding construction of circumcentre of a triangle?

• A. The circumcentre of a triangle is the point in the plane equidistant from the three vertices of the triangle
• B. The circumcenter is the point of concurrency of the three altitudes of each side from opposite vertex of the triangle.
• C. The circumcenter is the point of concurrency of the three perpendicular bisectors of each side of the triangle.
• D. None of these

Answer 1

Answer: (A), (C)

The circumcentre of a triangle is the point in the plane equidistant from the three vertices of the triangle
The circumcenter is the point of concurrency of the three perpendicular bisectors of each side of the triangle.

Circumcircle passes through the vertices of the triangle , so its circumcenter is equidistant from all the vertices.

So option $A$ is correct.

By definition circumcentre is the point of intersection of perpendicular bisector of sides of triangle.

So option $C$ is also correct.