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max area of ABCD, intersectons of circle , y=x^2 1990 Kyiv City MO 10.5

Source:

July 18, 2021
geometrymaxgeometric inequalityanalytic geometryparabolaarea

Problem Statement

A circle centered at a point (0,1)(0, 1) on the coordinate plane intersects the parabola y=x2y = x^2 at four points: A,B,C,D.A, B, C, D. Find the largest possible value of the area of ​​the quadrilateral ABCDABCD.
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