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.


A) Make CD and FE intersect. What is FG*GE? What is CG*GD? B) What do you notice about those two values? Did you expect that? Why or why not? 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.


A) What is Arc 1 + Arc 2? What is one half of that? B) How does that value compare to the angle in the middle? Did you expect that? C) Restate the theorem in your own words.