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Source: 2021 AIME II P5

March 19, 2021
geometryAMCAIMEAIME II

Problem Statement

For positive real numbers ss, let τ(s)\tau(s) denote the set of all obtuse triangles that have area ss and two sides with lengths 44 and 1010. The set of all ss for which τ(s)\tau(s) is nonempty, but all triangles in τ(s)\tau(s) are congruent, is an interval [a,b)[a,b). Find a2+b2a^2+b^2.
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