Question 203603
a tangent is perpendicular to the radius at the point of tangency
___ so you need to find the distance from the point to the line, to find the radius of the circle
___ you already have the center, so the equation is (x-6)^2 + (y-7)^2 = r^2


5x + 24 = 20y ___ (1/4)x + 6/5 = y ___ the slope of the given line is 1/4


so the slope of the radius line (perpendicular) is -4


equation of radius line ___ (y - 7) = -4 (x - 6) ___ y = -4x + 31


substituting to find intersection ___ x/4 + 6/5 = -4x + 31


clearing fractions ___ 5x + 24 = -80x + 620 ___ 85x = 644 ___ x = 644/85


substituting ___ y = (1/4)(644/85) + 6/5 ___ y = 263/85


using the distance formula ___ r^2 = [6 - (644/85)]^2 + [7 - (263/85)]^2 = (-134/85)^2 + (332/85)^2 = 1508/85