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AIME 2025 I / An isosceles trapezoid has an inscribed circle tangent to each of its four…

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question

An isosceles trapezoid has an inscribed circle tangent to each of its four sides. The radius of the circle is 3, and the area of the trapezoid is 72. Let the parallel sides of the trapezoid have lengths rr and ss, with r≠sr \neq s. Find r2+s2r^{2}+s^{2}.
Plain-text mathematical notation (without MathML)
An isosceles trapezoid has an inscribed circle tangent to each of its four sides. The radius of the circle is 3, and the area of the trapezoid is 72. Let the parallel sides of the trapezoid have lengths r and s, with r≠s. Find r²+s².
Original LaTeX notation
An isosceles trapezoid has an inscribed circle tangent to each of its four sides. The radius of the circle is 3, and the area of the trapezoid is 72. Let the parallel sides of the trapezoid have lengths $r$ and $s$, with $r \neq s$. Find $r^{2}+s^{2}$.

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Source and history

task_id
ce05f6da-e95a-53dc-a204-debf0d083c50
task_key
AIME2025~2dI--test--ce05f6da-e95a-53dc-a204-debf0d083c50
task_revision_id
3
config / split
AIME2025-I / test

Official source

initial import