I am trying to place a node at the intersection of two lines, however I do not obtain the desired result.
I would like the circled x in the pciture below to appear on the intersection of the two lines. What am I doing wrong?

mwe:
\documentclass{article}
\usepackage{tikz}
\usepackage[active,tightpage]{preview}
\usetikzlibrary{intersections}
\PreviewEnvironment{tikzpicture}
\begin{document}
\begin{tikzpicture}
\node (l3) at (-1,-2) {test};
\node (c1) at (intersection of (0,0)-- ++(300:7) and {l3.north--++(99,0)})[draw, circle]{x};
\draw (0,0)-- ++(300:3) (l3.north)--++(4,0);
\end{tikzpicture}
\end{document}
EDIT Explanation, why I need the different syntax: I am creating a picture like this:

I draw and adjust the text nodes by hand, afterwards I need to draw the horizontal lines into the triangle. I decided to be to lazy to use pgfmath, with the chosen awnser I can write the following to generate the horizontal lines:
\foreach \level in {nodeL1, nodeL2, ...} {
\coordinate (c1) at (intersection of 0,0--[shift={(300:7)}]0,0 and \level.north--[xshift=99]\level.north);
\coordinate (c2) at (intersection of 0,0--[shift={(240:7)}]0,0 and \level.north--[xshift=99]\level.north);
\draw (c1) -- (c2);
};



intersection of-Syntax WITHOUT named paths not working with relative coordinates (see Qrrbrbirlbel s awnser) – ted Jun 23 '13 at 18:39(intersection of 0,0--300:7 and l3.north--[xshift=4cm]l3.north). – Kpym Apr 30 '18 at 14:01