Problem of the week 4

[Math Tutor]

Let T be an external point for the acute-angled ▲ABC and the sections MN, PQ, KL are parallel to the sides AB, BC, CA and they pass trough the point T and their ends are on the sides of the triangle. Prove that
MT.TN + PT.TQ + PT.TL ≤ R², where R is the radius of the circumference prescribed around the ▲ABC.

[Math Tutor]

The problem is provided by http://www.math10.com/forumbg/profile.p ... file&u=536