A circle C has center at the origin and radius 9. Another circle K has a diameter with one end at the origin and the other end at the point (0,17). The circles C and K intersect in two points. Let P be the point of intersection of C and K which lies in the first quadrant. Let (r,theta) be the polar coordinates of P, chosen so that r is positive and 0

Question

A circle C has center at the origin and radius 9. Another circle K has a diameter with one end at the origin and the other end at the point (0,17). The circles C and K intersect in two points. Let P be the point of intersection of C and K which lies in the first quadrant. Let (r,theta) be the polar coordinates of P, chosen so that r is positive and 0<theta<2 inclusive. Find r and theta.

Damon · Answer

Triangle with two sides of length 8.5 and one of length 9
side 1 origin to (0,8.5 ), length 8.5
side 2, (0,8.5) to P, length 8.5
side 3, origin to P, length 9 (this is r of course)

find angle in triangle at origin
cos A = 4.5/8.5
find A from that
then
Theta = 90-A in degrees or pi/2 - A if using radians