MathDB
Geo(graphy) Reading Passage

Source: 2022 AIME I #8

February 9, 2022
AMCAIMEAIME Igeometry

Problem Statement

Equilateral triangle △ABC\triangle ABC is inscribed in circle ω\omega with radius 18.18. Circle ωA\omega_A is tangent to sides AB‾\overline{AB} and AC‾\overline{AC} and is internally tangent to ω\omega. Circles ωB\omega_B and ωC\omega_C are defined analogously. Circles ωA\omega_A, ωB\omega_B, and ωC\omega_C meet in six points−-two points for each pair of circles. The three intersection points closest to the vertices of △ABC\triangle ABC are the vertices of a large equilateral triangle in the interior of △ABC\triangle ABC, and the other three intersection points are the vertices of a smaller equilateral triangle in the interior of △ABC\triangle ABC. The side length of the smaller equilateral triangle can be written as a−b\sqrt{a}-\sqrt{b}, where aa and bb are positive integers. Find a+ba+b.
Back to ProblemsView on AoPS