Question 389721
  <pre><font size = 3 color = "indigo"><b>
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)   
{{{drawing(300,300, -6, 6, -6, 6, grid(1),
circle(0, 0,4),
circle(2.828, -2.828,0.3),
line(0,0,2.828,-2.828),
circle(-2.828, 2.828,0.3),
line(0,0,-2.828,2.828),


graph( 300, 300, -6, 6, -6, 6))}}}