Find the radius r of the circle which has center (5,0) and is tangent to the line y = 2x.

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Is the point of tangency given in the question?

no the point of tangency is not given

Given the tangent line y =2x

So slope of the line perpendicular to the tangent line containing the radius (5,0) will be

-1/2

so the equation of the perpendicular line is y -0 = -1/2 (x-5)

y = -1/2 (x-5)

To find the point of tangency, equate y = 2x to y = -1/2 (x-5)

so 2x = -1/2 (x-5)

-4x = x-5

-5x= -5

x=1

so y =1*2 = 2

so the point of tangency = (1,2)

so radius^2 = (1-5)^2+ (2-0)^2

= 16 +4 =20

so radius r = sqrt(20) = 2 sqrt(5)

Please let me know if you have any questions and best me if you are satisfactory.

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