由 bugzpodder 於 星期三 十一月 05, 2003 10:40 am
Solution by Michael Lipnowski
Let ABC be such at triangle where MA*MB*MC<=2
Let A be the largest angle, and let the angle bisector of A intersect the circle at M. Suppose A >60, then we can find B' C' on the minor arc BC such that <MB'A=<MC'A=30, ie B'AC' is equilateral => MB'*MC'*MA=2
But MB'<MB, MC'<MC which implies MB*MC*MA >2, a contradiction
therefore the largest angle is at most 60 degrees => ABC is equilateral