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.