5.3 Notes Bisectors in Triangles

Concurrent When three or more lines intersect at one point, they are concurrent The point at which they intersect is the point of concurrency

The perpendicular bisectors of the sides of a triangle are concurrent at a point equidistant from the vertices Theorem 5-6 Concurrency of Perpendicular Bisectors Theorem

The point of concurrency of the perpendicular bisectors of a triangle is called the circumcenter of the triangle. The circle is circumscribed about the triangle Circumcenter

What are the coordinates of the circumcenter of the triangle with vertices P (0,6), O (0,0), and S (4,0) Finding the Circumcenter of a Triangle

What are the coordinates of the circumcenter of the triangle with vertices A (2,7), B (10,7), and C (10,3) Finding the Circumcenter of a Triangle #2

The bisectors of the angles of a triangle are concurrent at point equidistant from the sides of the triangle Theorem 5-7 Concurrency of Angle Bisectors Theorem

The point of concurrency of the angle bisectors of a triangle is called the incenter of the triangle. The circle is inscribed in the triangle Incenter

Identifying and Using the Incenter of a Triangle

Identifying and Using the Incenter of a Triangle #2

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