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Sorry for another noob question...

I have three (could be more if necessary but it think three is enough) lines which are all intersected by another line. I know the distance between the points of intersection. I need to find the equation of the line.

The full problem is actually in 3D space with 9 points, 9 lines and known lengths between the intersections.

I'm struggling with the 2D problem so help with either would be appreciated! diagram

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    Given a point on a line and a distance from that point on that line, there are two possible points on that line which fulfill this. Given three lines, there are a total of six points to consider. One must check every combination of a point on line one with a point on line two with a point on line three (8 possibilities in all) to see if a line can be drawn through those points. Off hand, I'm not sure a unique solution is guaranteed. – 2017-02-14

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In this question, there are totally 4 unknowns to be found and they are $x_4, y_4, x_6, y_6$.

From the fact that $(x_4, y_4)$ lies on $y = m_1x + c_1$, we get one equation (which is $y_4 = m_1x_4 + c_1$) in two unknowns $x_4$ and $y_4$.

Similarly, we have the second equation in $x_6$ and $y_6$ in terms of $m_3$ and $c_3$.

Similarly, via $(x_5, y_5) = (\dfrac {x_4 + x_6}{2}, \dfrac {y_4 + y_6}{2})$, we get the third equation.

From the distance between $(x_4, y_4)$ and $(x_6, y_6) = 2a$, we get the fourth equation.

Since each of these equations has non-related known values involved, they should be independent. The required values can therefore be found, through messy computations.