Problem 296

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?


给定整数边三角形ABC,其三边满足BC ≤ AC ≤ AB。

有多少个周长不超过100 000的三角形ABC使得BE的长为整数?