Tangent and Secant of a Circle

A tangent is a line that connects with the circle at just one point, while a secant is a line that intersects the circle at two points. It is a specific type of secant which occurs when the two endpoints of the secant’s chord come together at a single point.

Aspect

Tangent of Circle

Secant of Circle

Definition

Tangent of circle cuts the circle at only one point.

Secant of circle cuts the circle at two points.

Pass Through Circle

Tangent never passes through circle.

Secant passes through the circle.

Intersection of Points

Tangent never intersects two points.

Secant intersects with two points.

Perpendicular to Radius

Tangent is perpendicular to the radius of the circle.

Secant of the circle may or may not be perpendicular to the circle.

Secant of a Circle

Secant of a circle is a fundamental concept in geometry that can be described as a straight line intersecting the circle at two distinct points. In this article, we will understand the definition, properties, theorems, and real-world examples surrounding the concept of secants.

In this article, we will learn about the meaning of secant, the formula to calculate the secant of a circle, properties, Intersecting secants, tangent of a circle, theorem of the secant of a circle, the difference between secant, tangent, and chord, and real-life examples of Secant of a Circle.

Table of Content

  • What is a Secant of a Circle?
  • Formula of Secant of a Circle
  • Properties of Secant of a Circle
  • Tangent and Secant of a Circle
  • Secant of a Circle Theorem
  • Examples of Secant of a Circle

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What is a Secant of a Circle?

A secant of a circle is a straight line that intersects the circle at two distinct points. When this line crosses a circle, it enters the interior of the circle, creating two points of intersection on the circle itself. Essentially, a secant line connects two points on the circle’s circumference by passing through its interior. It’s important to note that a straight line can intersect any given circle at a maximum of two different points, and when it does, it is referred to as a secant line to that circle....

Formula of Secant of a Circle

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Intersecting Secants

When two secant lines cross or intersect inside a circle, they are referred to as intersecting secants. In simple terms, intersecting secants are two straight lines that both cut through the circle and meet or cross each other within the circle’s boundaries. This interaction creates points of intersection and various geometric relationships within the circle, including the formation of chords, central angles, and the division of the circle into segments....

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Secant of a Circle Theorem

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Real-Life Examples of Secant of a Circle

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Examples of Secant of a Circle

Example 1: Consider a circle with a radius of 5 units. Draw a secant line from a point outside the circle, intersecting the circle at points A and B. If the external part of the secant measures 8 units, find the length of the secant segment within the circle....

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Q1. In a circle with a radius of 7 units, a secant line is drawn from a point outside the circle. If the external part of the secant measures 10 units, find the length of the secant segment within the circle....

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