Proofs to two inequality conjectures for a point on the plane of a triangle

Abstract

Abstract We prove two conjectures for a point on the plane of a triangle presented in (Liu in J. Math. Inequal. 8(3):597-611, 2014, doi: 10.1007/s11590-013-0708-4 ) by using the successive difference substitution algorithm NEWTSDS. Compared with the original proof, the new one is simpler and more easily understood. Similar problems can be treated with the same procedure.

Keywords

• geometry inequality
• successive difference substitution
• automated reasoning