Secant of a Circle Theorem
Various theorem related to Secant of a Circle Theorem are added below,
I. Tangent Secant Theorem
Tangent-Secant Theorem states that when you draw a tangent segment and a secant segment from an external point to a circle, the square of the length of the tangent segment is equal to the product of the length of the secant segment and its outer portion.
In a formula: (AB)2 = AC × AD
Learn, Tangent Secant Theorem
II. Intersecting Secants Theorem
The Intersecting Secants Theorem states that if two secant segments are drawn from a point outside a circle, then the product of the length of one secant segment and its outer portion is equal to the product of the length of the other secant segment and its outer portion.
In a formula: MN × MO = MP × MQ
This theorem is applicable when you have two intersecting secants, such as MO and MQ in the provided figure, and it establishes a relationship between the lengths of these secant segments and their external portions.
III. Secant and Angle Measures
When two secant lines intersect inside a circle, the measure of each angle formed is half the sum of the measures of the arcs intercepted by those secants. In simpler terms, if you have two secant lines like AD and BC intersecting inside the circle at point O, then the size of the angle AOB is equal to half the sum of the lengths of the arcs AB and CD.
m∠AOB = 1/2(AB + CD)
Whereas, when two secant lines intersect outside the circle, the measure of the angle formed by these lines is half the positive difference between the measures of the intercepted arcs. For instance, in the circle with intersecting secant lines AC and AE outside the circle at point A, the angle CAE is equal to half the positive difference between the lengths of the arcs CE and BD.
m∠CAE = 1/2(CE – BD)
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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