the vertex of the measure angle is on the edge of the circle. The vertex will be doubled to find the measure of the arc, or the central angle. Any two vertextes may be placed inside the circle and they will alway share the same arc measure if the endpoints are the same.

touches the circle at one point, will nevr e inside the circle, it will only ever touch the outside of the circle. The point of tangency. a radius touching a tangent will always make a 90 degress angle.