MathDB

6

Part of 2018 International Zhautykov Olympiad

Problems(1)

izho2018 p6 (geometry)

Source: izho 2018

2/14/2018
In a circle with a radius RR a convex hexagon is inscribed. The diagonals ADAD and BEBE,BEBE and CFCF,CFCF and ADAD of the hexagon intersect at the points MM,NN andKK, respectively. Let r1,r2,r3,r4,r5,r6r_1,r_2,r_3,r_4,r_5,r_6 be the radii of circles inscribed in triangles ABM,BCN,CDK,DEM,EFN,AFK ABM,BCN,CDK,DEM,EFN,AFK respectively. Prove that.r1+r2+r3+r4+r5+r6≤R3r_1+r_2+r_3+r_4+r_5+r_6\leq R\sqrt{3} .
geometryinequalitiesgeometric inequality