Incenter Assignment (Posted on 2011-03-23)

	Submitted by Bractals
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Let uppercase letters denote points in the plane and lowercase letters denote the real numbers assigned to the points. Let A and B be arbitrary distinct points in the plane. Construct the regular hexagon ABCDEF and let G denote the intersection of rays CD and FE. The points F and E are symmetrical to the points C and D about the bisector of angle DGE. Therefore, the triangles GDF and GEC have the same incenter. thus, (g+d+f)/3 = (g+e+c)/3 or d+f = e+c. Triangles ACE and BFD have the center of the hexagon as their incenter. Thus, (a+c+e)/3 = (b+f+d)/3 or a = b. Therefore, all points in the plane are assigned the same real number.

	Subject	Author	Date
	re(3): Solution. Hope this makes sense.	Gamer	2011-03-23 19:20:14
	re(2): Solution. Hope this makes sense.	Jer	2011-03-23 17:03:55
	re: Solution. Hope this makes sense.	Bractals	2011-03-23 16:12:28
	Solution. Hope this makes sense.	Jer	2011-03-23 13:31:32