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congruent triangles if r, R, and area are equal >

Source: VI Soros Olympiad 1990-00 R2 10.4 https://artofproblemsolving.com/community/c2416727_soros_olympiad_in_mathematics

May 28, 2024
geometrycongruent triangles

Problem Statement

Can we say that two triangles are congruent if the radii of the inscribed circles, the radii of the circumscribed circles, and the areas of these triangles are equal?