Problem 296

Angular Bisector and Tangent

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`.

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

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