Maths Olympiad Prep

Track / Stage 5 / 110 of 400 #710 of 1964

Problem 710

AIME late
Geometry Difficulty 5.2 Prove it

(ISR 1) Prove that the product of two sides of a triangle is always greater than the product of the diameters of the inscribed circle and the circumscribed circle.

This one wants a proof. Work it on paper, then read the official solution and mark yourself. Be honest about it: the record is only any use to you if it is.

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Official solution

None

Source: NuminaMath-1.5, licensed Apache-2.0. Statement reproduced verbatim; metadata (topic, difficulty, ordering) added by this project.