In the diagram shown below, AC is tangent to circle O at A and to circle P at C, OP intersects AC at B, OA = 4, AB = 5, and PC = 10.
The measure of angle AOB = ? degrees
The measure of angle PCB = ? degrees
The measure of line segment BC =
Since triangle(OAB) is a right triangle (tangents are perpendicular to radii drawn to the point of contact), tan(AOB) = 5/4 --> angle(AOB) = tan-1(5/4) = ...
Since AC is a tangent and PC is a radius drawn to the point of tangency, angle(PCB) = ...
Triangle(OAB) is similar to triangle(PCB), so OA / PC = AB / BC.