Find Scalene Non-Right Triangle 3rd Point w/ Side Lengths & Coordinates

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pjhphysics
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If I know the length of all three sides of a triangle and the coordinates of two of those points, how can I find the coordinates of the third point (in a scalene non-right triangle)?

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If this problem is too hard, then let's try something easier.

If you have a point X, and you have a length d, can you find all points whose distance from X is d?
 
Yes, so I have to find the intersection of two circles. How is this achieved?
 
"intersection of two circles", means you have the equation (implied by the problem description) of each circle and you want to know what point they have in common. Two equations and two unknowns.