## Τετάρτη, 11 Οκτωβρίου 2017

### 2002 JBMO Shortlist 10

Let ${ABC}$  be a triangle with area ${S}$  and points ${D,E, F}$  on the sides ${BC,CA,AB}$. Perpendiculars at points ${D,E, F}$  to the ${BC,CA,AB}$  cut circumcircle of the triangle ${ABC at points (D_1,D_2), (E_1,E2), (F_1, F_2) }$. Prove that: ${|D_1B \cdot D_1C - D_2B \cdot D_2C| + |E_1A \cdot E_1C – E_2A \cdot E_2C| + |F_1B \cdot F_1A - F_2B \cdot F_2A| > 4S }$

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