© 2014 IEEE. We present a simple and powerful technique for testing with a prescribed precision whether a set of 2D lines meet at a given point. The method is based on a probabilistic framework and has a fundamental geometric interpretation. We use this technique for detecting vanishing points in images. We developed a very simple algorithm that yields state-of-the-art results at a much lower computational cost than its competitors. The presentation of the proposed formulation is complemented with numerous examples.