7

Part of 1968 IMO Shortlist

Problems(1)

Product of the radii of three circles doesn't exceed A

Source:

Prove that the product of the radii of three circles exscribed to a given triangle does not exceed

A=\frac{3\sqrt 3}{8}

times the product of the side lengths of the triangle. When does equality hold?

trigonometrygeometric inequalityTriangleIMO Shortlist