A fur dresser had to put a patch shaped like a scalene triangle on a piece of fur. Suddenly he realized he had made a terrible mistake. The patch fitted the hole but the fur side faced the wrong way.
The fur dresser, after some thought, cut the triangular patch into 3 parts, each of which would be unchanged when turned over. How?
(In reply to
re: Half an answer by SilverKnight)
"I thought a triangle's circumcenter MUST lie within the triangle...."
Nope. An obtuse triangle has its circumcenter outside. Right triangles have theirs in the middle of the hypotenuse. For strictly acute triangles, the circumcenter is inside and since it always is the common point where all three perpendicular bisectors of the side meet, it is clear that it is equidistant from each of the pairs of vertices.
We still have the open question of whether there is a point inside an obtuse triangle such that this point is equidistant from each of the vertex pairs. I doubt it.
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Posted by Richard
on 2004-05-28 14:34:53 |
re(2): Half an answer
