Problem 419: Triangle, Cevian, Incircle, Excircle, Inradius, Exradius, Congruence

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The figure shows an isosceles triangle ABC with AB = BC = 5/7AC. The inradius of triangle BEC and the exradius of triangle ABE are equal to 17. Find the inradius of triangle ABC. Post a comment or solution.
 

Isosceles triangle, incircle, radius, congruence, inradius
 

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