On a sheet of paper draw a circle of radius 1 inch, and call the center of that circle O. Pick a point P which is 2.5 inches away from 0. Draw the circle which has OP as a diameter, as in the picture on the right in Figure 1.1.6. Let A be one of the points where this circle intersects the first circle. Draw the line through P and A. In general the tangent line through a point on a circle is perpendicular to the line joining that point to the center of the circle (why?). Use this fact to explain why the line you drew is the tangent line through A and to calculate the length of PA. Does it match the physical measurement of PA?