This type of problem has been showing up more and more often on the Calculator test. I have personally seen it on a region test, district test, and a few invitational tests.
If the circle is inside the isosceles triangle, then the radius can be found using 1/2*b*sqrt((2a-b)/(2a+b)) where a is the smallest side and b is one of the congruent sides.
-Kevin
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