Prove or disprove, that the points of intersection of the adjacent trisectors of the angles of any triangle are the vertices of an equilateral triangle. (In other words, that for any yellow triangle, the green triangle will be equilateral, given that the thinner lines trisect their respective angles.)

(In reply to re: baa by LDoc)

REASONING:
(A+B+C=180)/3 = A/3 + B/3 + C/3 =120
if you add this with the given equations, you can come up with:

A/3= Z-60 [or] Z= 60 + A/3
B/3= X-60 [or] X= 60 + B/3
C/3= Y-60 [or] Y= 60 + C/3

okay, now the annoying part...

X + A/3 + C/3 =180 (sub in found values)
X + (Z-60) + (Y-60) =180

X + Y + Z =300

really REALLY annoying part next:

Posted by LDoc on 2002-11-07 18:07:05