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The Circumcenter. Concurrent. What three or more lines are when they intersect at one point. The three lines shown to the left are concurrent. Point of Concurrency. The point where three or more concurrent lines intersect. The yellow dot is the point of concurrency.
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Concurrent What three or more lines are when they intersect at one point The three lines shown to the left are concurrent.
Point of Concurrency The point where three or more concurrent lines intersect The yellow dot is the point of concurrency.
Circumcenter of a triangle The point of concurrency of the perpendicular bisectors of the triangles The yellow dot is the circumcenter of the triangle. http://www.mathopenref.com/trianglecircumcenter.html
Right triangle Circumcenter Rule However, if the triangle you are trying to find the circumcenter of happens to be a right triangle, then the circumcenter is always the midpoint of the hypotenuse, as proved below.
Theorem 5-6 The perpendicular bisectors of the sides of a triangle are concurrent at a point equidistant from the vertices. Basically, if you you draw a segment from the circumcenter, G, to the vertices of the triangle, the segments formed are congruent.
Circumscribed about a Triangle When you have a triangle, the circumcenter of the triangle can be used as the origin of a circle that circumscribes the triangle, and passes through each of the three vertices. As seen to the right, point O, the circumcenter, is used as the origin for the circle circumscribing ∆ABC.
