From an exterior point P that is h units from a circle of radius r, a tangent line is drawn to the circle. Let y denote the distance from the point P to the point of tangency T.
(a) Express y as a function of h. (If C is the center of the circle, then PT is perpendicular to CT).
(b) If r is the radius of Earth and h is the altitude of a space shuttle, then y is the maximum distance to Earth that an astronaut can see from the shuttle. In particular, if h=200 mi and r=4000 mi, approximate y.

Question

From an exterior point P that is h units from a circle of radius r, a tangent line is drawn to the circle. Let y denote the distance from the point P to the point of tangency T. 
(a) Express y as a function of h. (If C is the center of the circle, then PT is perpendicular to CT).
(b) If r is the radius of Earth and h is the altitude of a space shuttle, then y is the maximum distance to Earth that an astronaut can see from the shuttle. In particular, if h=200 mi and r=4000 mi, approximate y.