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izho2018 p6 (geometry)

Source: izho 2018

February 14, 2018

geometryinequalitiesgeometric inequality

Problem Statement

In a circle with a radius

M

a convex hexagon is inscribed. The diagonals

N

and

BE

,

BE

and

CF

,

CF

and

AD

of the hexagon intersect at the points

M

,

N

and

K

, respectively. Let

r_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

respectively. Prove that.

r_1+r_2+r_3+r_4+r_5+r_6\leq R\sqrt{3}

.

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