An eficient rndomized agorithm for line and circle detection in the Conformal Geometric Algebra framework is designed and implemented. This arithmetic performs well when an image has strong background noise. In conformal geometric algebra, circle and line in conformal space can be represented as multivectors. Then the distance would be more easily computed from each edge point to the hypothesis by this detecting algorithm. Based on these distances, the matched points are efficiently summarized and aggregated to yield the true object. The experimental evaluation achieves excellent performance in the hypotheses voting and yields competitive results.