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Angular Bisector and Tangent

Problem 296

Published on Friday, 11th June 2010, 01:00 pm; Solved by 372

Given is an integer sided triangle ABC with BCACAB.
k is the angular bisector of angle ACB.
m is the tangent at C to the circumscribed circle of ABC.
n is a line parallel to m through B.
The intersection of n and k is called E.

How many triangles ABC with a perimeter not exceeding 100 000 exist such that BE has integral length?