Let ABCDEFGHIJKL be a regular 12sided polygon. TRUE or FALSE: The diagonals AE, CF, and DH
intersect in a point.
Each of the 12 angles is 10*180º/12= 150º
Call the possible point of crossing M
Consider triangles DEM and FEM. If M really is a point then EM will be the same length in each.
Angles MED and MDE are both 45º so DEM is 90º. So EM is √2/2 times the side length.
Angle FME is 30º and MEF is 105º so FEM is 45º. Using the law of sines, EM is √2/2 times the side length.
So the answer is TRUE

Posted by Jer
on 20130823 20:17:56 