square and angles problem

• Oct 8th 2010, 02:27 AM
bloo.tomarto
square and angles problem
hey guys

A---------E----F----B
|..........................|
|..........................|
|..........................|
|..........................|
|..........................|
C-------------------D
ABCD is a aquare

Prove angle ACE is half angle FCD

thanks guys
• Oct 8th 2010, 07:50 AM
Opalg
Quote:

Originally Posted by bloo.tomarto
hey guys

A---------E----F----B
|..........................|
|..........................|
|..........................|
|..........................|
|..........................|
C-------------------D
ABCD is a aquare

Prove angle ACE is half angle FCD

thanks guys

Presumably E is meant to be halfway between A and B; and F is halfway between E and B?

In that case, use some trigonometry to find the tan of each of those angles, and check that they are related by the formula $\displaystyle \tan2\theta = \dfrac{2\tan\theta}{1-\tan^2\theta}.$ As an extra hint, draw a vertical line from F down to the side CD, in order to create a right-angled triangle containing the angle FCD.