Section 5.3: Bisectors in Triangles

when three or more lines intersect at one point

when the circumcenter is used as the center of a circle that contains each vertex of a triangle

the point at which concurrent lines intersect

point of concurrency of the perpendicular bisectors of a triangle

when the incenter is used as the center of a circle that contains exactly one point of each side of a triangle

point of concurrency of the angle bisectors of atriangle

Section 5.3: Bisectors in TrianglesObjective: To identify properties of perpendicular bisectors and angle bisectors

Example 1: Finding the Circumcenter of a TriangleWhat is the center of the circle that you can circumscribe about a triangle with vertices A(3, 5), B(0, 0) and C(8, 0)?

Quick Check:

What are the coordinates of the circumcenter for the triangle with vertices A(2,7), B(10,7), and C(10,3)?

0°118

0°104

Section 5.3: Bisectors in TrianglesObjective: To identify properties of perpendicular bisectors and angle bisectors

Example 2: Using a CircumcenterA civil engineer wants to install a cell phone tower that is equidistant from the mall, the airport, and the subway. How should the civil engineer determine where to build the tower?

Quick Check:

A town planner wants to place a bench equidistant from the three trees in the park. Where should they place the bench?

0°72

0°118

Section 5.3: Bisectors in TrianglesObjective: To identify properties of perpendicular bisectors and angle bisectors

Example 3: Identifying and Using the Incenter of a TriangleGB = 8x - 7 and GD = 5x + 8. What is GF?

Quick Check:

QN = 5x + 36 and QM = 2x + 51. What is QO?

Is it possible for QP to equal 50? Explain.

A

B

C D E

FG

K

NP

LMJ

O

Q

Incenter

0°

48