MathDB
Possible values of an expression

Source: Baltic Way 2014, Problem 5

November 11, 2014
geometrytrigonometrycyclic quadrilateralalgebra proposedalgebra

Problem Statement

Given positive real numbers a,b,c,da, b, c, d that satisfy equalities a2+d2−ad=b2+c2+bc  and  a2+b2=c2+d2a^2 + d^2 - ad = b^2 + c^2 + bc \ \ \text{and} \ \ a^2 + b^2 = c^2 + d^2 find all possible values of the expression ab+cdad+bc.\frac{ab+cd}{ad+bc}.
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