Secant of a Circle

To learn about the Secant of a circle, let’s recall what a circle is. A circle is a closed loop. In a circle, every point on the circle is at an equal distance from the centre O. In a secant, the line intersects the circle at two points. But a tangent intersects the circle at only one point around its outer line. This is the basic difference between a secant and a tangent. But the common fact between them is both the lines are drawn from outside of the circle. Let us learn more here.

Secant of the Circle Definition

A straight line that intersects a circle in two points is called a secant line. A chord is the line segment that joins two distinct points of the circle. A chord is in a unique secant line and every secant line defines a unique chord. In geometry, a secant is a line that cuts any curve in at least two different points. Secant means ‘to cut’ extracted from a Latin word ‘secare’. While in a circle, a secant will touch the circle in exactly two points and a chord is the line segment defined by these two points, that is the interval on a secant whose endpoints are these two points.

Secant of a Circle Formula

If a secant and a tangent of a circle are drawn from a point outside the circle, then;

Lengths of the secant × its external segment = (length of the tangent segment)2

Diameter of Circle – Secant

A secant is an extension of a chord in a circle which is a straight line segment of which the endpoints lie on the circle. If the same chord passes through the centre of the circle, then it is a diameter. So an extended Diameter is a secant.

Intersecting Secants

When two secants of a circle intersect each other at a point outside the circle, there becomes an intersecting relationship between those two line segments.

If PQ and RS are the intersecting secants of the given circle then ( P + Q). Q = (R + S) .S

Secant of a Circle

In the above figure, you can see:

  • Blue line segment is the secant
  • Red shows the tangent
  • Green is the chord of circle

 

How do you find the secant of a circle?

Secant intersects the circle exactly at two points. The measure of an angle formed by a tangent and a secant or two secants or two tangents which intersect outside the circle is one half the positive difference of the measures of the intercepted arcs.

Difference between a secant and a chord

A part of a line between the two endpoints is called a line segment.

Secant Chord
It intersects the circle at two points It touches the circle at two points
It is drawn from outside the circle It lies within the circle

Register at BYJU’S to learn more on other mathematical topics in a fun and engaging way.

Leave a Comment

Your email address will not be published. Required fields are marked *