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?

These problems are part of Project Euler and are licensed under CC BY-NC-SA 2.0 UK