Given three concentric (having the same center) circles.
Their radii are 1,2 and 3.
Place three points A,B,C - each on a different circle to get a triangle ABC
with a maximal area.
What is this area?
without loss of generality we can place the point on the circle of radius 1 at (0,1), thus the remaining points can be considered at
(2cos(x),2sin(x)) and (3cos(y),3sin(y))
the area of this triangle is given by
Using Mathematica's Maximize function under the contstraints
it gives the maximum area of 9.8094 with x=3.95901 and y=5.77539
bellow is a link to a picture of the 3 circles along with this triangle
Posted by Daniel
on 2010-09-09 17:34:17