1. 5-3 Bisectors in Triangles
Centers of Triangles (this does not mean that the points we find have to be on the interior of the triangle)
-Circumcenter
-Incenter

2. Concurrent Point of concurrency
When three or more lines intersect at one point.
The point at which the three or more lines intersect at.
Point of concurrency

3. This point of concurrency for the perpendicular bisectors of a triangle is referred to as the circumcenter of the triangle.

4. Since the circumcenter is equidistant from the vertices, you can use the circumcenter as the center of the circle that contains each vertex of the triangle. You say the circle is circumscribed about the triangle.
Circumscribed Circle Applet

5. The circumcenter can be inside, on, or outside the triangle.
In an acute triangle it is inside
In a right triangle it is on (it will be on the hypotenuse)
In an obtuse triangle it is outside.

6. s
Anything on line s will be equidistant from H&M and anything on line t will be equidistant from E&H. t

7. Suppose that the three major cities of Cleveland, Columbus, and Pittsburgh wish to develop an advanced medical facility that is to service each city’s population, where is the best location for such a facility?

8. The point of concurrency of the angle bisectors is called the incenter of the triangle.
For any triangle the incenter is always inside the triangle. The location of the incenter will always be equidistant from the three sides of the triangle (measuring with perpendicular segments from a point to a line of course). The incenter is the center of the circle that can be inscribed in the triangle. (to be inscribed you have to be tangent to each side of the polygon)

10. If you have three trees that need watered and you are using a rotating sprinkler at what point would you place the sprinkler so that each tree gets watered.

11. We have a triangular section of garden that is surrounded by sidewalks, where should a sprinkler be placed in efforts to water as much of the garden as possible yet keep the sidewalks dry?