The link below gives the equations for the line that tangent. Once you have that, finding the normal should be straightforward.
http://mathworld.wolfram.com/CircleTangentLine.html
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a tangent is a line that touches the circle at only ONE point
A tangent of a circle is a straight line that touches the circle at only one point.
The tangent secant angle is the angle between the tangent to a circle and the secant, when the latter is extended.
A tangent to a circle is a line from a point outside the circles which touches the circle at a single point.
A tangent of a circle is a straight line that touches the circle's circumference at just one point.