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min of max sidelength of an inscribed quadrilateral in circle of radius 1

Source: 2005 Indonedia MO Province P2 q1

December 11, 2020
geometrycyclic quadrilateralgeometric inequality

Problem Statement

The length of the largest side of the cyclic quadrilateral ABCDABCD is aa, while the radius of the circumcircle of △ACD\vartriangle ACD is 11. Find the smallest possible value for aa. Which cyclic quadrilateral ABCDABCD gives the value aa equal to the smallest value?
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