1. 5.2: Circumcenters and Incenters
Objectives:
To know and apply the properties of circumcenters.
To know and apply the properties of incenters.

2. Vocabulary:

3. 5.2: Circumcenters and Incenters
Activity:
Need:
2 pieces of patty paper.
A pencil or felt tip pen (2 colors preferably)
A strait-edge (ruler)
Glue stick to share with a partner
On your patty paper:
 Draw an isosceles triangle on each paper
 Draw an acute triangle on each paper
 Draw a right triangle on each paper
 Draw an obtuse triangle on each paper

4. 5.2: Circumcenters and Incenters
Activity:
Label each paper:
 bisector
 bisector

5. Perpendicular Bisectors
of a triangle…
bisect each side at a right angle
meet at a point called the circumcenter
The circumcenter is equidistant from the 3 vertices of the triangle.
The circumcenter is the center of the circle that is circumscribed about the triangle.
The circumcenter could be located inside, outside, or ON the triangle. C

6. Find all measures that are possible in the figure.
Using the Circumcenter…. Example 1
Find all measures that are possible in the figure.

7. Example 2: Finding the Circumcenter of a Right Triangle
Find the circumcenter of ∆HJK with vertices H(0, 0), J(10, 0), and K(0, 6).
Step 1 Graph the triangle.
Step 2 Draw in two
perpendicular bisectors.
Step 3 Find the intersection of
the 2 lines.
Answer: the circumcenter is at (5, 3)!
Now complete: page 311 #12 – 17, 20 (10 minutes!)

8. Now complete: page 311 #12 – 17, 20

9. Angle Bisectors Paste-able! of a triangle… bisect each angle
meet at the incenter
The incenter is equidistant from the 3 sides of the triangle.
The incenter is the center of the circle that is inscribed in the triangle.
The incenter is always inside the circle. I

10. QX and RX are angle bisectors of ΔPQR. Find the distance from X to PQ.
Example 1
QX and RX are angle bisectors of ΔPQR.
Find the distance from X to PQ.
Find mPQX.

11. Example 2
2. JP, KP, and HP are angle bisectors of ∆HJK. Find the distance from P to HK.

12. Now complete: page 311 #12 – 32