1. Perpendicular to a line from a point

2. Bisector of an angle

3. Point on the bisector is equidistant from the sides of the angle

4. Perpendicular bisector of a segment

5. Point on the perpendicular bisector is equidistant from the endpoints of the segment

6. Pedal triangle of a point

7. Antiparallels – cyclic quadrilateral

8. Angles of antiparallels

9. Angle bisectors of a triangle are concurrent

10. Incenter of a triangle

11. Pedal Triangle of the incenter

12. The incenter of a triangle is the circumcenter of its pedal triangle.

13. Perpendicular bisectors of the sides of a triangle are concurrent

14. Circumcenter of a triangle

15. Pedal Triangle of the circumcenter

16. The circumcenter of a triangle is the orthocenter of its pedal triangle.

17. Altitudes of a triangle area concurrent

18. Orthocenter of a triangle

19. Pedal triangle of the orthocenter

20. The orthocenter of a triangle is the incenter of its pedal triangle

21. Time ’ s Up! About your speaker: – Name: Michael Keyton – Company: IMSA – Email: keyton@imsa.edu – Social Media: Yes – Quick bio: Family (1 wife, 2 sons, 2 cats), Interests: Mathematics (Geometry), Golf, Baseball (Texas Rangers), Music (Symphony), Philosophy (Phenomenology), Literature/History