What are the measures of the apex angles of all isosceles triangles with circumradius 9 and inradius 4?

(As a reminder, the circumradius is the radius of the circumscribed circle, and the inradius is the radius of the inscribed circle.)

(In reply to An almost complete estimated solution (spoiler) by Grate Guy)

Nice pictures! I drew the same ones by hand using compasses, marked ruler and protractor. First I drew a circle of radius 9, then a diameter of it, and finally the 1/2 angles at the apex using the protractor.  The radius of the incircle was then easily confirmed as 4.

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Posted by Richard on 2006-07-06 17:12:09