**Problem 9**

The construction
begins with three lines that intersect to form _{}. Choose a point D on ray _{} so that _{} is longer than _{}, _{}, and _{}. Draw a circular arc starting at point D, using the point A
as center, until it hits_{}. Label this point E.
Draw another circular arc starting at point E, using the point C as
center, until it hits _{}. Label this point F. Continue drawing circular arcs around
the figure using the natural point as the center to get the following figure in
which _{} = _{},_{} = _{}, _{} = _{}. Prove _{} = _{}.

[Problem
submitted by Kevin Windsor, LACC Instructor of Mathematics.]

**Solution for Problem 9:**

By
construction the following statements are true:

_{} = _{} + _{}, _{} = _{} + _{}, and _{} = _{} è _{} + _{} = _{} + _{}.

_{} = _{} + _{}, _{} = _{} + _{}, and _{} = _{} è _{} + _{} = _{} + _{}.

_{} = _{} + _{}, _{} = _{} + _{}, and _{} = _{} è _{} + _{} = _{} + _{}

Also, _{} = _{}

and _{} = _{}.

Add the left sides and rights side to form the equation:

_{}+_{}+_{}+_{}+_{}+_{}+_{}+_{} = _{}+_{}+_{}+_{}+_{}+_{}+_{}+_{}

+_{}_{}++_{}+_{}+_{}+_{}+_{} = _{}+_{}+_{}+_{}+_{}+_{}_{}++_{}_{}

Thus,
_{} = _{}.