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Before going to the application, let us first understand what a secant is.
A line is said to be a secant of a circle if it intersects the circle at two different points. The Latin term ‘secare’, which means to cut, is where we get the English word secant. It is also possible to think of it as the portion of the chord of a circle that extends beyond the boundaries of the circle itself. The secant of a circle is the line that traverses the circle and meets it at two different places along its path.
The Chord vs. Secant Difference in Classical Terms
We get a chord at the two sites of intersection when a secant line cuts the circle in two different places at the same time. A line segment that has endpoints that are on the arc of a circle is known as the chord of the circle. In other terms, a chord is a segment of a line that joins two points on the circumference of the circle; however, if this cord is stretched on both sides, it transforms into the secant. The diameter is determined by the line of the secant that travels through the centre of the circle. As a result, the chord or diameter of a circle can be determined using a secant line.
Formula for the Secant of a Circle
If a secant and a tangent of a circle are drawn from the same point that is not inside the circle then it can be represented as,
Lengths of the secant × its external segment = (length of the tangent segment)2
Properties
A secant is a line that intersects a circle in exactly two points
The product of one entire secant segment and its external segment is equivalent to the product of the other whole secant segment and its external segment whenever two secants cross at an exterior point
It is possible for two secants to intersect either within or outside of a circle. We discover that the intersecting secants inside and outside the circles illustrated below form angles x and y at the places of intersection, respectively. On the basis of this characteristic of secants, there exist two different theorems. According to the theorem, we have the following:
Half of the total amount of the arcs that were intercepted forms the angle that is formed by the two secants that intersect inside the circle.
The angle that is created when two secants cross outside of a circle has a measure that is equal to half of the difference between the arcs that were intercepted.
The lines that cut the circle and continue on in both directions infinitely are called tangents and secants respectively. The main difference between a secant and a tangent is that a secant cuts the circle in two different places, while a tangent only does so in one place
If a secant and a tangent are drawn to a circle from a shared exterior point, then the square of the length of the tangent segment is equal to the product of the lengths of the entire secant segment and its external secant segment
Application
In the everyday world, a secant of a circle can be found in a variety of locations, specifically everywhere that circles or curves are present. The applications are-
while building curving bridges
determining the distance between the orbiting moon and the various sites on earth
Obscure geometric constructs can benefit from the secants useful application of a wide variety of fascinating features
Numerous theorems about circles can be proven by examining a circle’s secants and the secants that intersect with one another
When determining the difference in distance between two points, architects frequently use tangent graphs because of their versatility and widespread application in the field
Secants may be seen being used to measure and completely illustrate how electronic waves are in various ways of communication such as calling and texting. One illustration of this would be how secants can be seen being used in measuring how calls are made
Conclusion
A line is said to be a secant of a circle if it intersects the circle at two different points. This property along with the others that are mentioned in the above article are used in day to day life for while building curving bridges, determining the distance between the orbiting moon and the various sites on earth, and many more things are done by this.
