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This problem trains for: AMC-10, SAT-II, AMC-12.

What is the largest distance between any two points with polar coordinates:

equation

if

equation

All the points with such polar coordinates are points on the circumference of a circle with radius 5 units, in the second quadrant of the Cartesian plane.

The largest distance between two such points is realized when one of the points is on the y-axis and the other one is on the x-axis. Then,

equation