Hi,         

Note: tangent and radius are perpendicular

Pt(0,0) and Pt(x,y) 

the point where line with m = 1 is tangent: slope of radius segment = -1

 m = (y-0)/(x-0)

 -1 = y/x

 y = -x

 x^2 +y^2=16

      y  = sqrt(16-x^2) substituting -x for y

      -x = sqrt(16-x^2)

     x^2 = 16 - x^2

     2x^2 = 16

    x = ± sqrt(8) 

Points of tangency for the two parallel tangents with slope = 1 are

 (2.828,-2.828)  and (-2.828,2.828)   



 

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