When constructing the circumcenter and circumscribed circle of a triangle, you need to find the intersection of all three of which type of line?

A- medians

B- perpendicular bisectors

C- altitudes

D- angle bisectors

My choice is B.

correct

Thank you!! :)

Your choice is correct. When constructing the circumcenter and circumscribed circle of a triangle, you need to find the intersection of all three perpendicular bisectors.

To understand why, let's break down the options and explain how each type of line is related to constructing the circumcenter and circumscribed circle:

A- Medians: Medians are lines drawn from each vertex of a triangle to the midpoint of the opposite side. The intersection of the medians is known as the centroid, which does not necessarily coincide with the circumcenter.

C- Altitudes: Altitudes are lines drawn from each vertex of a triangle perpendicular to the opposite side. The intersection of altitudes is known as the orthocenter, which is not always the same as the circumcenter.

D- Angle bisectors: Angle bisectors are lines that divide the angles of a triangle into two equal parts. The intersection of angle bisectors is known as the incenter, which is distinct from the circumcenter.

So, the correct answer is B, perpendicular bisectors. Perpendicular bisectors are lines that are drawn through the midpoint of each side of the triangle and are perpendicular to those sides. The intersection of three perpendicular bisectors coincides with the circumcenter, which is the center of the circumscribed circle. Thus, by finding the intersection of these lines, you can locate the circumcenter and construct the circumscribed circle of the triangle.