Angular Bisector and Tangent
June 11, 2010
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?
Written by gamwe6 who lives and works in San Francisco building useful things. You should follow him on Twitter