Secant of a circle

To understand what the Secant of a circle is, we must first understand what a circle is. A circle is a closed loop that has been completed. Every point on a circle is at an equal distance from the circle’s centre, which is denoted by the letter O. In a secant, the line intersects the circle at two locations on either side of the line. A tangent, on the other hand, touches the circle at only one point around its circumference. The fundamental distinction between a secant and a tangent is as follows: However, there is one thing that they have in common: both lines are drawn from outside of the circle. A secant line is a straight line that intersects a circle at two locations on the circle’s circumference. A chord is a line segment that connects two locations on a circle that are not connected by any other line segment. A chord is contained within a single secant line, and each secant line creates a single chord. In geometry, a secant is a line that cuts any curve in at least two different places on either side of the line. Secant meaning ‘to cut’ from the Latin ‘secare’. Whereas in a circle, a secant will touch the circle in exactly two spots and a chord is the line segment defined by these two points, an interval on a secant whose endpoints are these two points is referred to as the interval on a secant whose interval is these two points.

Examples of the Secant of a Circle

In everyday life, we come across a secant of a circle in a variety of situations, particularly in situations where circles or curves are involved. The use of curved bridges, for example, or the determination of distances among different points on the planet are all examples of applications for this technique. Secants have a variety of intriguing features that can be used to aid in the development of complex geometric structures. Circle theorems based on the secants and the intersecting secants of a circle can be found in a variety of places.

Secant Theorems

As a result of two secants crossing at an exterior point, the product of one entire secant segment and its external segment is equal to the product of the other whole secant segment and its external segment, which is known as the intersecting secant theorem. This is referred to as the secant theorem or the secant power theorem in some circles.

It is possible to see that segments AB and AC are the two secant segments that intersect at point A in the diagram above. In the whole secant segment AB, AD is the external secant segment of the whole secant segment, and AE is the external secant segment of the secant segment AC. So, the theorem says AB × AD = AC × AE

Secant of a Circle Formula

If a secant and a tangent of a circle are drawn from a point outside the circle, then the following is true:

Secant lengths x external segment = (length of the tangent segment)2

Diameter of Circle – Secant

A secant is an extension of a chord in a circle that is a straight line segment with the endpoints of which are located on the circle. If the same chord runs through the centre of the circle, the circle is said to have a diameter. As a result, an expanded Diameter is referred to as a secant.

Intersecting Secants

When two secants of a circle cross each other at a place outside the circle, the intersecting relationship between those two line segments is defined as the intersection of those two line segments.

( P + Q). Q = (R + S) . S

What is a circle’s secant?

Secant intersects the circle exactly at two spots, as seen in the diagram. One-half the positive difference between the measurements of the intercepted arcs is used to calculate the measure of an angle formed by a tangent and a secant, or by two secants or two tangents that meet outside the circle.

The Tangent Secant Theorem

It is stated that, when two tangents and two secants are drawn to the same circle from the same exterior point, the product of the lengths of the complete secant segment and its external secant segment is equal to one-sixth the length of the tangent segment (the tangent secant theorem).

Take a look at the illustration above to see that:

Using the same outside point, the secant AC and the tangent CD are both drawn simultaneously. Secant segments are designated as AB (inside) and BC (exterior) (exterior). The product of the secant and its exterior segment is equal to the square of the tangent segment’s exterior segment’s product. AC × BC = CD2

The angle subtended by the tangent and secant at the exterior is equal to half the difference between the major arc and the minor arc intercepted by them on the interior.

Difference Between a Chord and a Secant

When a secant line cuts a circle at two locations, we get a chord at the two spots where the secant line and the circle intersect. The chord of a circle is a line segment whose endpoints are located on the circumference of the circle’s circumference. In the diagram above, the chord AB is a piece of the secant line QP, which is represented by the circle. For the sake of simplicity, consider the following definition: a chord is a line segment connecting two locations on the circumference of the circle, and when this chord is stretched on both sides, it is known as a secant. The diameter of a circle is determined by the secant line that runs through the centre of the circle. As a result, a secant line can be used to determine the chord or diameter of a circle.

Conclusion

Geometry is the study of shapes and their relationships. A circle is a planar structure made up of a closed curve in which each point on the curve is the same distance from the circle’s centre as the other points on the curve.

Tangent: A line formed from the centre of a circle through one end of a circular arc and ending at the other end of the circle is referred to as a straight line in geometry. The word secant derives from the Latin word secare, which literally means to cut. In the case of a circle, a secant intersects the circle at two places that are precisely the same.