Question: I am stuck with this problem. I posted an [earlier problem](https://math.stackexchange.com/questions/41257/find-remaining-vertices-of-a-square-given-2) with a square, where rotation with i of 90 degrees was possible. This one is a rhombus, how should I proceed?

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> Given ABCD is a rhombus with AC = 2BD, and b = 3 + i, d = 1 - 3i. Find a and c.
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Thanks for your help.

Answer: 
Hint: The points $A,C$ are the points of intersection between the diagonal $AC$ and the circle centered at the mid point of $BD$ with radius $|\frac{AC}{2}|$. How do you express this information in terms of Cartesian equations?
Hint: What is true about all the sides of a rhombus?