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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

r

and

s

, with

r \neq s

. Find

r^{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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task_id: ce05f6da-e95a-53dc-a204-debf0d083c50
task_key: AIME2025~2dI--test--ce05f6da-e95a-53dc-a204-debf0d083c50
task_revision_id: 2
config / split: AIME2025-I / test

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