This is not a general mathematics help site. In the future, please send mathematics questions to places set up to handle them.

The http://mathworld.wolfram.com/ web pages have a Contact the MathWorld Team link, usually at the bottom of the page.

The reference in the web page you listed,
Rhoad, R.; Milauskas, G.; and Whipple, R., Geometry for Enjoyment and Challenge, rev. ed. Evanston, IL: McDougal, Littell & Company, 1984,
or similar geometry text, is probably available in a library.

A vector geometry approach may be helpful. Let C be the circle center, r its radius. Let P be a point on the line v, a unit vector in the direction of the line. First, project C onto the line giving point Q l = (C - P).v, Q = P + l v**. Then compute the distance of C from the line d = ||(C - Q)|| If this distance d = r, then Q is the tangent point. If this distance d > r, then there are no real intersection points. Else, the distance of the intersection points from Q are found using Pythagoras. b = sqrt(r^2 - d^2) then the two intersection points are given by: ip1 = Q + b v, ip2 = Q - b v.