## Angular Bisector and Tangent

### Problem 296

Published on Friday, 11th June 2010, 01:00 pm; Solved by 379; Difficulty rating: 60%
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?