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About a Strengthened Version of the Erdos …
Forum GeometricorumVolume 17 (2017) 197 GEOMISSN 1534-1178 About a Strengthened Version ofthe Erd os-Mordell InequalityDan S tefan Marinescu and Mihai MoneaAbstract. In this paper, we use barycentric coordinates to prove the strength-ened Version of the Erd os-Mordell inequality, proposed by Dao, Ngyuen andPham in [3].One of the most beautiful results in geometry is represented by the Erd os-Mordell ([4]) inequality that for any pointPinside a triangleABC,PA+PB+PC 2d(P, AB) + 2d(P, BC) + 2d(P, CA),whered(P, AB)denotes the distance from the pointPto the lineAB. There area number of references on this result; see, for example, [1, 5]. Recently, Dao,Nguyen and Pham [3] improved the Erd os-Mordell inequality by replacing thelengthsPA,PB,PCby the distances fromPto the tangents to the circumcircleatA,B, aim of this paper is to prove a further Strengthened Version of the theoremof Dao-Nguyen-Pham.
About a strengthened version of the Erdos-Mordell inequality 201˝ Corollary 5. Let the incircle of triangle ABC touch the sides BC, CA, AB at A′
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