Finding the Diameter of a Cyclic Quadrilateral

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To find the diameter of a cyclic quadrilateral with sides 1, 2, 3, and d, Ptolemy's theorem and Brahmagupta's formula were attempted but did not yield results. The user seeks guidance on the correct approach to solve for d. A link to additional resources on cyclic quadrilaterals is provided for further assistance. The discussion emphasizes the need for effective methods to determine the diameter in this geometric context. Engaging with these mathematical principles can lead to a solution for the problem presented.
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Homework Statement


Given a cyclic quadrilateral with side lengths 1, 2, 3 and d (in that order) where d is the diameter of the circle, find d.


The Attempt at a Solution



I tried using Ptolemy's theorem and Brahmagupta's formula, but to no avail. Can I get pointed in the correct direction please?
 
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Maybe you can find something useful http://pballew.blogspot.com/2009/10/notes-on-cyclic-quadrilaterals.html" .
 
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Question: A clock's minute hand has length 4 and its hour hand has length 3. What is the distance between the tips at the moment when it is increasing most rapidly?(Putnam Exam Question) Answer: Making assumption that both the hands moves at constant angular velocities, the answer is ## \sqrt{7} .## But don't you think this assumption is somewhat doubtful and wrong?

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