A tangent of a circle is a straight line that touches or intersects the circle at only one point, and it never enters the circle's interior
. The point where the tangent meets the circle is called the point of tangency
. The tangent is perpendicular to the radius of the circle at the point of contact
. Some key properties of tangents to a circle include:
- A tangent can be drawn for any curved shape
- The point of tangency is the only point of intersection where the straight line touches the curve
- The tangent is perpendicular to the radius of the circle at the point of contact
There are two major theorems related to tangents to a circle:
- Theorem 1 : If two tangents are drawn from an external point of the circle, then they are of equal lengths
- Theorem 2 : The tangent to a circle is perpendicular to the radius of the circle at the point of contact
For example, consider a circle with center O and radius 6 cm. A tangent to the circle at point A meets the line OB such that OB = 10 cm. Using the Pythagorean theorem, the length of AB can be found, as the tangent is perpendicular to the radius of the circle at the point of contact
