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296. Angular Bisector and Tangent

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Given is an integer sided triangle ABC with BC ≤ AC ≤ AB.
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.

p296_bisector.gif

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

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