USAMTS Extension
by rrusczyk, Jun 17, 2006, 3:21 PM
After Sandor sent me the problem that became #5 on the second round of the USAMTS, I came up with the following based on it:
Given acute triangle ABC in plane
, a point Q in space is defined such that <AQB = <BQC = 90 degrees and <AQC = 120 degrees. Given triangle ABC, construct with ruler and compass the projection of point Q onto plane . (All constructions are to be done in plane .)
We considered this for a while for the USAMTS, then decided it might be a touch too evil, at least for round 2.
Given acute triangle ABC in plane
, a point Q in space is defined such that <AQB = <BQC = 90 degrees and <AQC = 120 degrees. Given triangle ABC, construct with ruler and compass the projection of point Q onto plane . (All constructions are to be done in plane .)We considered this for a while for the USAMTS, then decided it might be a touch too evil, at least for round 2.
February 2012
January 2012