1. 6.2 Bisectors of triangles

2. What we will learn Use and find circumcenter of a triangle
Use and find incenter of a triangle

3. Needed vocab
Concurrent: three or more lines, rays, or segments intersect in the same point
Point of concurrency: point of intersection of concurrent lines
Circumcenter: point of concurrency of the perpendicular bisectors of a triangle
Incenter: point of concurrency of the angle bisectors of a triangle

4. Ex. 2 Finding circumcenter
Find perpendicular bisectors of the horizontal and vertical sides
Point where they cross is circumcenter
Find circumcenter of triangle with vertices at A(0,3); B(0,-1); C(6,-1)
Use graph paper, easier

5. Ex. 3 using incenter 𝑁𝐷 =5𝑥−1 𝑎𝑛𝑑 𝑁𝐸 =2𝑥+11 Find NF
𝑁𝐷 =5𝑥−1 𝑎𝑛𝑑 𝑁𝐸 =2𝑥+11
Find NF
N is incenter by markings
𝑁𝐷 = 𝑁𝐸
5𝑥−1=2𝑥+11
−2𝑥+1−2𝑥+1
3𝑥=12
3𝑥 3 = 12 3
𝑥=4
𝑁𝐷 = 𝑁𝐹 Thm 6.4
So 𝑁𝐹 =19
Can NG be equal to 18?
Shortest distance to a side is a perpendicular segment
Since 18 is less than 19 and NF is 19, then no

6. Ex. 4 Using diagrams
A city wants to place a lamppost on the boulevard shown so that the lamppost is the same distance from all three streets.
Looking for incenter
Sketch is fine