Length of Tangent

# Length of Tangent

## Definition of Tangent

A tangent is a straight line that touches a curve at one point and goes off in a straight line. The point of contact is called the point of tangency.

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## Tangents Drawn to Circle from External Point (Length of Tangent Theorem):

A tangent is a line that touches a curve at a single point and is perpendicular to the curve at that point. The length of a tangent from an external point to a circle is the length of the hypotenuse of a right triangle whose other two sides are the radius of the circle and the point where the tangent intersects the circle.

## Length of Tangent Theorem:

The length of the tangent at a point on a curve is the length of the segment from the point to the curve.

## Length of Tangent Theorem Statement:

The length of a tangent to a circle is the length of the segment from the point of tangency to the center of the circle.

## Length of Tangents Example Problems:

1. Find the length of the tangent to the circle at the point (2, 3).

The tangent has a length of 5.

2. Find the length of the tangent to the circle at the point (5, 6).

The tangent has a length of 8.

## What is Length of Tangent on a Circle

A tangent is a straight line that intersects a circle at one point. The length of the tangent is the distance from the point of intersection to the circle.

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