A tangent of a circle is a line that touches the circle at exactly one point.[br][br][color=#6d9eeb]The blue circle on the left[/color] has a tangent on it, and[color=#93c47d] the green circle on the right [/color]has a line going through the circle, but it is not tangent to the circle.[br][br]The point T is called [i]the point of tangency[/i].

A circle is given below, with centre C, radius r. The radius r meets the circle at point P.[br][br]Draw a tangent line at the point P, and add a point on the tangent.[br][br]What is the angle between the tangent and the radius?

We know that the angle between the radius and tangent is 90º, and the Pythagorean Theorem tells us about right angle triangles. Consider this problem.[br][br]The line AB is tangent to the circle below, with A the point of tangency.[br][br]The radius (AC) has length 4, and the line AB has length 7.[br][br]What is the length of the line BC?