A new method for detecting circles with the characteristic of right triangle inscribed in a circle is proposed. Array storage space based on positions of valid pixels is constructed in order not to search triangles in image space but compressed arrays. By applying special searching algorithms, the complexity of the method is reduced. The procedure searches right triangles in storage space by grades, and then translates the calculation of circle parameters into triangles for the sake of avoiding repeated arithmetic operations and shortening running time. During the work, the proposed method polymerizes single circle parameters efficiently to get the final global results. Experimental results from composite and real images show the proposed algorithm can suppress noise interferences effectively when detecting circles in normal images. Compared with existing methods, it is faster, more reliable, and repeatable, and the accuracy is less than 1 pixel.