In triangle ABC, angle C has a measure of 60 degrees. Point D lies on side AC so that BD bisects angle B and BD = 1. Similarly, point E lies on side BC so that AE bisects angle A and AE = 2.
Find the area of triangle ABC.
(In reply to
re: Solution by Dennis)
I said the converse of
"If AE = 2BD, then angle B is a right angle"
is easy to prove.
I also had a problem showing that
"If AE = 2BD, then angle B is a right angle"
But, since a 306090 triangle meets the criteria of the problem, that's what I used.
I got
c^2 = a^2  ab + b^2
and
b(b + c  a)(a + c)^2 = 4a(a + c  b)(b + c)^2
and gave up.
EDIT
After a lot of calculations using the above two equations (which I never want to do again), I was able to show that b = 2a and c = a*sqrt(3).
Therefore, ABC is a 306090 triangle.
Edited on February 11, 2008, 11:52 pm
Edited on February 12, 2008, 2:18 pm

Posted by Bractals
on 20080211 20:47:24 