Tangent properties

Tangent Properties A tangent property is a relationship between the lengths of two radii of two circles that are tangent to each other. The tangent proper...

Tangent Properties

A tangent property is a relationship between the lengths of two radii of two circles that are tangent to each other.

The tangent property states:

The ratio of the length of the adjacent side to the length of the adjacent hypotenuse is equal to the ratio of the length of the opposite side to the length of the adjacent hypotenuse.

Examples:

In the picture below, the tangent property is illustrated. The length of AB is equal to the length of BC, and the length of AC is equal to the length of DC.

[Image of tangent property]

Another example is shown below. The tangent property can be used to prove that two circles are tangent.

[Image of circles tangent at two points]

The tangent property is a powerful tool that can be used to prove other theorems in geometry. It is used extensively in the study of circles and other curved shapes