If we choose three points at random on a circle of radius 1, what
is the
probability that they are the vertices of an obtuse triangle?

("At random" means three independent choices using the uniform 
distribution.  "Obtuse" means having one angle larger than 90
degrees.)


There will be a $1 prize for the best correct solution submitted
by a
midshipman.

A solution is "correct" if it answers the question correctly and
explains
the answer; a solution is "best" if it includes the clearest
correct
explanation.  Solutions are due by noon on Thursday, March 25,
1999.
Submit solutions to Prof. Hanna at mathprob@nadn.navy.mil, or via
the
mailbox in Chauvenet 301.

---------------------------
Correct solutions to Problem #89 (the polynomial with values 1/k)
came
from Midn 1/c Coleman (who used Maple) and Midn 3/c Estes (who
used a
TI-92).  P(10) = 1/5 and P(11) = 1.  Prize awarded at random to
Mr. Estes.
It's not too hard to answer the question without finding all the
coefficients of the polynomial, but there's no harm in using
powerful
technology if you have it.