One of the most important tasks in medical image analysis is segmentation. Its idea is to subdivide the image into regions in which each one contains components with similar properties. Image segmentation is typically used to locate objects and boundaries (lines, curves, etc.)in images. This approach is widely used in extracting tumour areas from medical images as a first step in therapy planning of cancer patients. The deformable Geodesic Active Contour (GAC) method is one of the most popular techniques used in object boundaries detection of images. In this work, we modify the automatic GAC technique by incorporating priori information extracted from the region of interest in an image. We introduce a new stopping function to speed up convergence and improve accuracy. The proposed technique was applied to both synthetic and real medical images. It has shown an improvement in speed of more than 40% together with an excellent accuracy compared to the traditional GAC model.