Tangent Circle Formula

Tangent Circle Formula

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“To touch” is what the term “tangent” signifies. “Tangere” is the Latin term for the same thing. A tangent is a line that meets the circle exactly at one point on its circumference and never enters the circle’s interior. Tangents to a circle can be many. They are parallel to the radius.

In geometry, the Tangent Circle Formula is a straight line that touches the circle just once. A tangent never penetrates the inside of the circle.

The tangent has two key properties:

  • A tangent intersects a circle at exactly one place.
  • The tangent makes a straight angle with the radius of the circle.

What Is Tangent Circle Formula?

A circle’s tangent is defined as a straight line that contacts the circle’s curve just once and does not enter the circle’s interior. The tangent makes a straight angle with the radius of the circle. The slope (m) and a point on the line are the two most important things to know while working with tangents. The tangent to a circle has the following generic Tangent Circle Formula:

The Tangent Circle Formula y = mx a √[1+ m2] gives the Tangent Circle Formula  x2 + y2 = a2 for a line y = mx + c. xa1 + yb1 = a2 is the tangent to the circle equation x2+ y2 = a2 at (a1, b1). This indicates that the tangent equation is xa1 + yb1 = a2, where a1 and b1 are the coordinates at which the tangent is formed.

The tangent has two key properties:

A tangent only hits a curve once.

A tangent is a line that never enters the inside of a circle.

At the point of tangency, the tangent makes a right angle with the radius of the circle.

Aside from the qualities described above, a tangent to the circle is related to mathematical theorems, which are utilised while doing significant computations in geometry. Let’s go through a few tangents to circle theorems in depth.

Examples using Tangent Circle Formula

Example questions based on the Tangent Circle Formula must be solved. Tangent Circle Formula problems of all varieties should be practised regularly. Students are encouraged to tackle Tangent Circle Formula questions using the Extramarks learning platform. Extramarks provide solutions to help students who are incorrectly applying the Tangent Circle Formula. It is essential to continue practising questions from all chapters of the Mathematics curriculum. Pure mathematics emphasises the existence and uniqueness of solutions, whereas practical mathematics emphasises the logical justification of procedures for approaching solutions. 

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FAQs (Frequently Asked Questions)

1. What is a circle's tangent?

A tangent is a line that never enters the inside of a circle. Tangent to the circle is defined as a straight line that is perpendicular to the radius and goes through a point on a circle. A circle tangent contacts the circle at one point, but does not enter its interior.

2. What Is the Tangent Circle Formula?

In geometry, a tangent of a circle is a straight line that touches the circle just once. The tangent formula is the Tangent Circle Formula, which is y = mx±a √[1+ m2] if the tangent is expressed in the slope form, and xa1 +y b1 = a2 if the tangent is represented in the two-point form.

3. What are the advantages of employing the Tangent Circle Formula?

Students can practice and review their homework using the Tangent Circle Formula. Providing all necessary concepts and equations in the right order saves time when referencing. The Tangent Circle Formula encourages students to think logically. The Tangent Circle Formula is quite useful for studying or answering questions.