Transcription of New Interpolation Inequalities to Euler’s R 2
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New Interpolation Inequalities to Euler’s R 2
Forum GeometricorumVolume 17 (2017) 149 GEOMISSN 1534-1178 New Interpolation Inequalities to euler sR 2rDorin Andrica and Dan S tefan MarinescuAbstract. The purpose of this paper is to obtain some Interpolation inequalitiesto the well-known euler s inequalityR 2rin terms of new geometric ele-ments given by the radiiRA,RB,RCof the tangent circles at the vertices to thecircumcircle of a triangle and to the opposite sides. The main results are givenin Theorems IntroductionAt the first 2015 Romanian IMO Team Selection Test the first author of thispaper has proposed the following problem: LetRAbe the radius of the tangentcircle atAto the circumcircle of triangleABCand to the sideBC.
New interpolation inequalities to Euler’s R≥2r 151 Proof 2. Let γAbe the circle tangent at A to the circumcircle of triangle ABC and tangent at T to the line BC. Assume that R = 1, and consider the inversion of pole
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