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,
= .