Point of Tangency

The point where the line touches the curve is called the point of tangency. The tangent to a curve touches the circumference of the curve only at the point of tangency. For the circle point of tangency is the point on the circumference of the circle, from which the tangent line passes. The radius drawn from the point of tangency to the centre of the circle is always perpendicular to the radius of the circle.

  • From the above figures, the line is tangent to the circle and the point of tangency is P.

Tangent to a Circle

Tangent in Circles are the line segments that touch the given curve only at one particular point. Tangent is a Greek word meaning “To Touch”. For a circle, we can say that the line which touches the circle from the outside at one single point on the circumference is called the tangent of the circle.

A circle can have many tangents but at a particular point on the circumference of the circle, only one tangent passes through that point on the circle. The tangent to a circle is always perpendicular to the radius of the circle.

In this article, we will learn about tangents to a circle, the equation of tangent, their properties, theorems, and examples.

Read in Detail: Circles

Table of Content

  • What is Tangent to a Circle?
    • Tangent to a Circle Definition
  • Tangent to a Circle
  • Point of Tangency
  • Equation of Tangent to a Circle
  • Condition of Tangency
  • Properties of Tangent
  • Tangent Theorems
    • Tangent Radius Theorem
    • Two Tangents Theorem
  • Tangent Formula
  • Solved Examples on Tangents to a Circle
  • Practice Problems on Tangent to a Circle

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What is Tangent to a Circle?

We define tangent as the line drawn from the external point that passes through a particular point on the curve. Examples of tangents are the lines that represent the velocity of the particle performing uniform circular motion at any instant. We can have many tangents to a curve but from a particular point, only a maximum of two tangents can be drawn to the curve....

Tangent to a Circle

A line that touches the circle exactly at one point is called the tangent of the circle. We can also define the tangent as the line which tells the direction of the point at a particular point that is performing uniform circular motion around a particular point (centre of the circle)....

Point of Tangency

The point where the line touches the curve is called the point of tangency. The tangent to a curve touches the circumference of the curve only at the point of tangency. For the circle point of tangency is the point on the circumference of the circle, from which the tangent line passes. The radius drawn from the point of tangency to the centre of the circle is always perpendicular to the radius of the circle....

Equation of Tangent to a Circle

We can easily find the equation of the tangent to a circle. The various equations of tangents are:...

Condition of Tangency

A line is called the tangent to the circle only if touches the circle only at one point else it is simply called the line intersecting the circle. On the basis of the Point of tangency, we divide the condition for tangent into three categories....

Properties of Tangent

Various properties of the tangent to a circle are...

Tangent Theorems

We have two important theorems on the tangent of a circle....

Tangent Formula

If we take any point P outside the circle and draw a tangent at point S on the circumference of the circle. Also, take a secant PQR such that QR is the chord of the circle then,...

Solved Examples on Tangents to a Circle

Example 1: In the given circle with centre O and AB is tangent to the circle. The radius of the circle is 5 cm. Find the length of the tangent AB if OP is given to be 13 cm....

Practice Problems on Tangent to a Circle

1. Find the equation of the tangent to the circle x2 + y2 = 25 at the point (3, 4)....

FAQs on Tangent to a Circle

What is the Meaning of Tangent in Circles?...