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5-3 Bisectors in Triangles. Concurrency. When three or more lines intersect at one point, they are concurrent . The point at which they intersect is the point of concurrency .
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Concurrency • When three or more lines intersect at one point, they are concurrent. • The point at which they intersect is the point of concurrency. Concurrency of Perpendicular Bisectors Theorem: The perpendicular bisectors of the sides of a triangle are concurrent at a point equidistant from the vertices.
Circumcenters • The point of concurrency of the perpendicular bisectors of a triangle is called the circumcenter. • You can use the circumcenter to circumscribe the triangle. • The circumcenter of a triangle can be INSIDE, ON, or OUTSIDE the triangle.
Finding the Circumcenter of a Triangle • What are the coordinates of the circumcenter of the triangle with vertices P(0, 6), O(0, 0), and S(4, 0)?
Incenters Concurrency of Angle Bisectors Theorem: The bisectors of the angles of a triangles are concurrent at a point equidistant from the sides of the triangle. • The point of concurrency of the angle bisectors of a triangle is called the incenter. • The incenter is the center of the circle that can be inscribed in the triangle.
Using the Incenter of a Triangle • GE = 2x – 7 and GF = x + 4. What is GD?
