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 = + = + .

= + , = + , and = + = + .

= + , = + , and = + = +

Also, =

and = .

 

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

+++++++ = +++++++

 

+++++++ = +++++++

 

Thus, = .