I think I may have come up with something, but it still doesn't seem as simple as vohonam would suggest it should be. I'm still looking for a cleaner solution... but my brain hurts too much right now. Here's some thought:

Draw bisecting line of C so that it intersects line AB. Call intersecing point F. Now draw line BE and EF. Because CF bisects BCE and that BC = EC, then:

1. BE is perpendicular to CF.
2. Triangle BEC is isosceles
3. angle CBE = angle BEC.
4. EF = BF
5. angle BEF = angle FBE

So, with these facts, plus:
6. angle BDE = 2 * angle BAC
7. the sum of the angles in a triangle is 180 degrees
8. the angles of a four-sided polygon is 360

There IS a way to show that angle BAC = 20 degrees.
I just need to clean up my chicken scratches.

Posted by Happy on 2002-06-20 17:18:20