Tangent to a Circle A tangent is a line segment that touches the circle at one point, called the center . The distance from the center to the point of...
A tangent is a line segment that touches the circle at one point, called the center. The distance from the center to the point of intersection is called the radius. The line segment connecting the center and the point of intersection is called the radius.
A tangent can be drawn to a circle from any point on the circle. For example, consider the point A on the circle with coordinates (2, 3). A tangent line segment can be drawn from point A to the center of the circle.
Another important fact about tangents is that they are perpendicular to the radius. This means that the angle formed by the tangent and the radius is always 90 degrees.
Here are some additional properties of tangents:
A tangent line segment intersects the circle at only one point.
The distance from the center to the point of intersection of the tangent and the circle is equal to the radius.
A tangent line segment is the only line segment that intersects the circle in exactly one point.
A circle can have an infinite number of tangents passing through its center.
Examples:
Consider the point (4, 5) on the circle. The tangent line segment from this point to the center would intersect the circle at the point (0, 0).
Consider the radius with the center at the origin. A tangent line segment from the point (1, 0) to the origin would intersect the circle at the point (1, 0).
Consider the circle with center at (0, 0) and radius 5. The tangent line segment from the point (3, 4) to the center would intersect the circle at the point (3, 4).
Tangents are important in many areas of mathematics, including geometry, trigonometry, and calculus. They are used in various applications such as finding the area of a circle, calculating the distance from a point to the center of a circle, and constructing geometric shapes