Proof of an inequality conjecture for a point in the plane of a triangle. (English) Zbl 1370.51017
Summary: In [J. Math. Inequal. 8, No. 3, Article ID 44, 597–611 (2014; Zbl 1305.51016)], J. Liu established a novel inequality about an arbitrary point in the plane of a triangle. He also put forward a conjecture about a parameterized version of this inequality. In this paper, we proceed to give a proof of this inequality facilitated by a combination of computeraided calculations and traditional planar geometry. This proof demonstrates again the strengths of the real algebra methodology developed over time by Ritt, Wu, Yang, Yang, Xia, et. al.
MSC:
51M16 | Inequalities and extremum problems in real or complex geometry |
51N20 | Euclidean analytic geometry |