In a triangle ABC, two lines are drawn that together trisect the angle at A. These intersect the side BC at points P and Q so that P is closer to B and Q is closer to C. Determine the smallest constant k such that ∣PQ∣≤k(∣BP∣+∣QC∣), for all such triangles. Determine if there are triangles for which equality applies. geometrygeometric inequalitytrisector