MathDB

5

Part of 2004 Turkey MO (2nd round)

Problems(1)

Turkey NMO 2004 P.5, Nice Geometric Inequality

Source:

12/11/2010
The excircle of a triangle ABCABC corresponding to AA touches the lines BC,CA,ABBC,CA,AB at A1,B1,C1A_1,B_1,C_1, respectively. The excircle corresponding to BB touches BC,CA,ABBC,CA,AB at A2,B2,C2A_2,B_2,C_2, and the excircle corresponding to CC touches BC,CA,ABBC,CA,AB at A3,B3,C3A_3,B_3,C_3, respectively. Find the maximum possible value of the ratio of the sum of the perimeters of △A1B1C1\triangle A_1B_1C_1, △A2B2C2\triangle A_2B_2C_2 and △A3B3C3\triangle A_3B_3C_3 to the circumradius of △ABC\triangle ABC.
inequalitiesratiogeometryperimetercircumcircletrigonometrygeometry proposed