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?