MathDB
Inequality in Geometry 2

Source: TST 2014 of Tajikistan

May 20, 2014
inequalitiesgeometrycircumcirclegeometric transformationreflectiongeometry proposed

Problem Statement

Let MMbe an interior point of triangle ABCABC. Let the line AMAM intersect the circumcircle of the triangle MBCMBC for the second time at point DD, the line BMBM intersect the circumcircle of the triangle MCAMCA for the second time at point EE, and the line CMCM intersect the circumcircle of the triangle MABMAB for the second time at point FF. Prove that ADMD+BEME+CFMF≥92\frac{AD}{MD} + \frac{BE}{ME} + \frac{CF}{MF} \geq \frac{9}{2}.
Proposed by Nairy Sedrakyan
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