Find a point on a given segment such that the distance from the 2 perpendicular segments on its sides to that point are equal.

Question

I don't know how else to phrase this problem. I am really curious what are the steps to solving this problem.

In case you did not understand what the problem is about, I'll try to explain better: There is a horizontal segment of known length and at its sides there's two perpendicular segments(poles) of known lengths as well. I need to find a point on the horizontal line such that the distance from the top of the poles to x are equal.

Answer 1

Let the point $p$ divides the segment in two parts with lengths denoted by $x$ and $l-x$

We denote the length of poles by $a$ and $b$

You construct two right triangles whose hypotenuses should be equal.

Thus $$a^2+x^2=b^2+(l-x)^2$$ Solve for $x$ to get $$x=\frac {b^2+l^2-a^2}{2l}$$