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Problem 296

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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?

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角平分线和切线

给定整数边三角形ABC，其三边满足BC ≤ AC ≤ AB。
k是角ACB的角平分线。m是ABC的外接圆在点C处的切线。n是过点B平行于m的直线。
n和k的交点记为E。

有多少个周长不超过100 000的三角形ABC使得BE的长为整数？

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