If we draw the line from the origin to (4, 1), it passes through (x, y) on the circle. (x, y) will be the closest point on the circle to (4, 1). The slope of the line is 1/4, so y/x = 1/4, or x = 4y. x and y satisfy x2 + y2 = 1, so (4y)2 + y2 = 1, 17y2 = 1, so y = approximately 0.243 and x = approximately 0.97.
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