1||0|116|0|
0|0|0|||||Morley%27s theorem. little error on comment on proof by Zsolt|Amic|1|10:57:13|01/31/2008|On this page %3A%0D%0A%0D%0Ahttp%3A%2F%2Fwww.cut-the-knot.org%2Ftriangle%2FMorley%2FMorleyZsolt.shtml%0D%0A%0D%0AI read%0D%0A%22%0D%0AThere are two special cases that should be mentioned. There is the case a %3D b %3D c %3D 20%2C when the theorem is obvious. The other case is when two of a%2C b%2C c add up to 40 without being equal. In this case%2C two of the six points coincide but the other four are distinct so the triangle ABC can still be constructed from them.%0D%0A%22%0D%0A%0D%0AThere is a mistake %3A the other case is when a or b or c%3D30%2C and in fact we cannot define the line joining two points which are the same...%0D%0A%0D%0AAnd I don%27t see why the case a%3Db%3Dc%3D20 is a special case...%0D%0A%0D%0ASo in my opinion this proof is wrong for a triangle ABC with a right angle.
1|1|0|||||RE%3A Morley%27s theorem|alexb||12:14:46|01/31/2008|You are right on both accounts%3A the special case is when one of the angles is 30%B0%2C not when all of them are equal or two add up to 40%B0.%0D%0A%0D%0AIn the exceptional case%2C the proof needs an amendment%3A one of the lines should be drawn not through two points %28which coincide and do not determine a line%29 but through a %28double%29 point at computable angles to the bases of the two adjacent trapezoids.%0D%0A%0D%0AI made a remark to that effect at the bottom of the page.%0D%0A%0D%0AMany thanks for bringing this up.