Angles and Secants P1.

Drag the green dots around to see the theorems and equations at work.
THEOREM: If two chords intersect in a circle, the product of the lengths of the segments of one chord equal the product of the segments of the other.
(1)
A) Make CD and FE intersect. What is FG*GE? What is CG*GD?[br]B) What do you notice about those two values? Did you expect that? Why or why not?[br]C) Restate the theorem in your own words.
THEOREM: The measure of an angle formed by two lines that intersect inside a circle is half the sum of the measures of the intercepted arcs.
(2)
A) What is Arc 1 + Arc 2? What is one half of that?[br]B) How does that value compare to the angle in the middle? Did you expect that?[br]C) Restate the theorem in your own words.
– Ms. Matlock

Information: Angles and Secants P1.