1. Constructions
Incenters

2. the incenter Note you only need 2 angle bisectors
The three angle bisectors are concurrent
at a point called …..
the incenter
Note you only need 2 angle bisectors
to locate the incenter.

3. the distance from the incenter to each side is the same.
Construction all 3 angle bisectors demonstrates that they are indeed concurrent lines.
Look at the red segments.
Note
the distance from the incenter to each side is the same.

4. The incenter is
the center of the inscribed circle.

5. Start with an angle bisector at vertex A.
Swing arc from A across angle A.

6. Next, swing arc from
the top intersection point
across the middle of the angle.

7. Next, repeat the process from the lower intersection point.

8. Now construct the ray through point A and the intersection points of the blue arcs.

9. ? Next, swing an arc across angle B.
Swing arc for angle bisector of vertex B.

10. Next,
Swing arc from the lower intersection point.

11. Next,
Swing arc from the upper intersection point.

12. Now construct the ray through point B and the intersection points of the blue arcs.

13. Incenter A Smile and a Fish.
To obtain the distance from the incenter and 1 of the sides you need..
A Smile
and a Fish.

14. We have the smile.

15. We have the FISH.

16. We also have the inscribed circle.
After shortening the perpendicular bisector we have the altitude.

17. Review of Incenter To inscribe a circle:
Construct the bisectors of 2 angles.
Label the intersection of the 2 rays as the incenter
To inscribe a circle:
We find the distance from the incenter to one of the sides by
The Smile and Fish approach.
Set the compass to the perpendicular distance, then construct the circle from the incenter.

18. Review of Altitude A Smile and a Fish.
To construct a perpendicular line through either an external or an internal point the technique is called…
A Smile
and a Fish.

19. C’est fini. Good day and good luck. A Senior Citizen Production
That’s all folks.
A Senior Citizen Production