I was aked to solve the following problem:
Guiven three lenghts and a triangle ABC, from every vertex whe draw one of the three lenghts, find the conditions such that the three lenghts meet in one point.
Then I suposed that at least two lenghts and a side makes a triangle, supose that the side is AB and the two lenghts meets at P, then using the cosine theorem to the triangle ABC and tha traingle ABP and I get a very large expression involving only lenghts, but it was very complex, and I think it can be simplified. Then my question is, if there is a synthetic solution to the problem. Please I don't want a full solution. Thanks.
