Question

Which of the following are properties of the circumcenter of a triangle? Check all that apply.

A.) The circumcenter of a right triangle falls on the side opposite the right angle
B.) The circumcenter is at the intersection of the perpendicular bisectors of the triangle's sides
C.) The circumcenter of a triangle is always inside it
D.) The circumcenter is equidistant from each vertex of a triangle

Answer 1

The true properties are:

A.) The circumcenter of a right triangle falls on the side opposite the right angle

B.) The circumcenter is at the intersection of the perpendicular bisectors of the triangle's sides

D.) The circumcenter is equidistant from each vertex of a triangle - The circumcenter of a triangle is the point which is equidistant from the three vertices of the triangle.

The false property is :

C.) The circumcenter of a triangle is always inside it - The circumcenter is not always inside the triangle. Its a point where all three lines intersect and its not necessary that it lies within the triangle.