What is the circumcenter of any given triangle?
The circumcenter of a triangle is the point at which the perpendicular bisectors of the triangle's three sides intersect. It is the center of the circumcircle, which is a circle that passes through all three vertices of the triangle. The circumcenter is equidistant from all three vertices of the triangle.
a) The point of concurrency of the altitudes of the triangle
b) The point of concurrency of the perpendicular bisectors of the sides of the triangle
c) The point of concurrency of the bisectors of the angles of the triangle
d) The point of concurrency of the medians of the triangle
a) The point of concurrency of the altitudes of a triangle is known as the orthocenter. The altitudes are the lines drawn from each vertex of the triangle perpendicular to the opposite side, and the orthocenter is the point where these three lines intersect.
b) The point of concurrency of the perpendicular bisectors of the sides of a triangle is called the circumcenter. The perpendicular bisector of a side is a line that is perpendicular to the side and passes through its midpoint. The circumcenter is the point where these three perpendicular bisectors intersect.
c) The point of concurrency of the bisectors of the angles of a triangle is called the incenter. The angle bisector of an angle in a triangle is a line that divides the angle into two equal angles. The incenter is the point where these three angle bisectors intersect.
d) The point of concurrency of the medians of a triangle is called the centroid. The median of a side of a triangle is a line that connects the midpoint of the side to the opposite vertex. The centroid is the point where the three medians of a triangle intersect.