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A tangent to a circle at the point (5,5) passes through the origin. The line with...

A tangent to a circle at the point (5,5) passes through the origin. The line with equation 3y=x+2 is a normal to the circle.

(i) Show all working, find the equation of the circle.

(ii) Find the coordinates of the point on the circle whih is nearest to the x-axis.
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