Greedy Geoff sawed off a corner of a brick shaped block of Christmas cake, exposing a triangular fresh face of moist rich delicious gateau. He placed the tetrahedral fragment on the table, with its fresh face downwards. He mused through a port laden haze that it looked very stable, just like a mountain in fact, with its summit above a point inside its (not necessarily equilateral) triangular footprint $ABC$. He decided to decorate it, and took a UKMT pennant flying from a toothpick, and stuck it at the summit, with the flagpole perfectly vertical. Of course, the port was still at work and he is a bit clumsy, so he jammed the toothpick right through the cake, stabbing it into the tablecloth at a point $X$. Show that the circles $ABX$, $BCX$ and $CAX$ all have the same radius.
3 Dimensional Geometry
1
$\begingroup$
geometry
3d
-
0I thought gato meant cat. – 2012-11-22
-
0http://en.wikipedia.org/wiki/Schl%C3%A4fli_orthoscheme – 2012-11-22
-
2Damn it, contest problem: http://www.mathcomp.leeds.ac.uk/ – 2012-11-22
-
0Alright, evidently a public contest problem from 2005: see http://meta.math.stackexchange.com/questions/6629/another-contest-problem – 2012-11-23
-
2Could you please make the title a little more descriptive? – 2012-11-23
-
1But of course the OP should say (if he knows) "contest problem from 2005". Then Will (and others, like me) won't get all excited about it's appropriateness for this forum. – 2012-11-23