# Finding the point of where three fixed-length lines intersect

We know the values of the coordinates (Xa,Ya), (Xb,Yb), and (Xc,Yc). We also know the lengths of A, B, and C. Is there a way (equation) to figure out the exact coordinates where the three lines A, B, and C intersect (the x? and y?).

I assume you could rotate all three of the lines until eventually they matched up.

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Yes. The point $(x,y)$ you want is on the following three circles :
$$C_a : (x-X_a)^2+(y-Y_a)^2={r_a}^2$$ $$C_b : (x-X_b)^2+(y-Y_b)^2={r_b}^2$$ $$C_c : (x-X_c)^2+(y-Y_c)^2={r_c}^2$$ where $r_a,r_b,r_c$ represents the lenght of $A,B,C$ respectively.
$C_a$ and $C_b$ have two intersection points at most. So, You can get the coordinate using the equation of $C_c$.