Tangent to a Circle
A tangent to a circle is a straight line which touches the circle at only one point. This point is called the point of tangency.
The tangent to a circle is perpendicular to the radius at the point of tangency.
In the circle , is a tangent and is the radius.
If is a tangent, then is perpendicular to .
For example, suppose units and units. Find the length of .
Because the radius is perpendicular to the tangent at the point of tangency, .
This makes the angle a right angle in the triangle and triangle a right triangle.
Now use the Pythagorean Theorem to find .
Since the length cannot be negative, the length of is units.