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?
给定整数边三角形ABC，其三边满足BC ≤ AC ≤ AB。