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Suppose a cyclic quadrilateral ABCDABCDABCD is such that
(i) AB=AD=1AB = AD = 1AB=AD=1,
(ii) CD=cos(∠ABC)CD = \cos(\angle ABC)CD=cos(∠ABC) and
(iii) cos(∠BAD)=−13.\cos(\angle BAD) = -\dfrac{1}{3}.cos(∠BAD)=−31.
Let RRR be the radius of the circle in which ABCDABCDABCD is inscribed. Find ⌊1000∗R⌋\lfloor 1000*R \rfloor⌊1000∗R⌋.
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