Which point is equidistant from vertices triangle

So it sounds like if we found the circumcenter that will be the answer to our problem. So if I want to find the point of concurrency of the three perpendicular bisectors we will have our circumcenter.

Now ideally I would have swung those arcs a little bit further apart but I can pick up where my two points are. So those two points are on my perpendicular bisector. So we found enough information to say that this point right here is equidistant from the three vertices. So I know that this has to be the radius of this circumscribed circle. All Geometry videos Unit Constructions. Next Unit Triangles. Brian McCall. Thank you for watching the video.

This circle is called the circumcircle. Names of standardized tests are owned by the trademark holders and are not affiliated with Varsity Tutors LLC. Media outlet trademarks are owned by the respective media outlets and are not affiliated with Varsity Tutors. Varsity Tutors connects learners with experts. Instructors are independent contractors who tailor their services to each client, using their own style, methods and materials.

Since a point equidistant from two points lies on the perpendicular bisector of the segment determined by the two points, the circumcenter labeled below is the point of concurrency of the three perpendicular bisectors of each side of the triangle. The basic construction of the circumcenter is to identify the midpoints of the original triangle. In the picture above the original triangle is triangle D ACD.

Then a perpendicular line was drawn through the midpoints perpendicular to the side segment. This particular example is of an acute scalene triangle.