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Areas in circumscribed quadrilateral

Source: 2022 Bulgarian Spring Math Competition, Problem 12.1

March 27, 2022
circumscribed quadrilateralareasgeometry

Problem Statement

ABCDABCD is circumscribed in a circle kk, such that [ACB]=s[ACB]=s, [ACD]=t[ACD]=t, s<ts<t. Determine the smallest value of 4s2+t25st\frac{4s^2+t^2}{5st} and when this minimum is achieved.
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