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2022 PUMaC Geometry A1 / B3

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September 10, 2023
geometryanalytic geometry

Problem Statement

Circle Γ\Gamma is centered at (0,0)(0, 0) in the plane with radius 202232022\sqrt3. Circle Ω\Omega is centered on the xx-axis, passes through the point A=(6066,0)A = (6066, 0), and intersects Γ\Gamma orthogonally at the point P=(x,y)P = (x, y) with y>0y > 0. If the length of the minor arc APAP on Ω\Omega can be expressed as mπn\frac{m\pi}{n} forrelatively prime positive integers m,nm, n, find m+nm + n. (Two circles intersect orthogonally at a point PP if the tangent lines at PP form a right angle.)
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