6

Part of 2010 Junior Balkan Team Selection Tests - Moldova

Problems(1)

E =\frac{a}{b + c}+\frac{b}{c + a}+\frac{c}{a + b} , right triangle, inradii

Source: 2010 Moldova JBMO TST p6

In a right triangle with the length legs

b

c

, and the length hypotenuse

a

, the ratio between the length of the hypotenuse and the length of the diameter of the inscribed circle does not exceed

1 + \sqrt2

. Determine the numerical value of the expression of

E =\frac{a}{b + c}+\frac{b}{c + a}+\frac{c}{a + b}

geometryalgebraGeometric Inequalitiesinequalities