In this paper, we present some new refinements of the Erdös-Mordell inequality, Barrow’s inequality, and Oppenheim’s inequality. Based on verification by computer, several related interesting conjectures are put forward.

In this paper, we present two sharpened versions of the Erdös-Mordell inequality and extend them to the cases with one parameter. As applications of our results, the Walker inequality and a new inequality in non-obtuse triangles are obtained. We also propose three interesting conjectures as open problems.