The image below is the end product of the constructions. Once the perpendicular bisector is created, it is easy to see the isoceles triangle that 'appears'. The tangent circle can be constructed using the intersection as the center point and by creating a segment from the center point to the point of tangency on the circle. This gives us the radius and completes our construction. You can scroll down to the next image to see a step by step construction using GSP.
