data-ad-format="horizontal">



 
Secant
From Latin: secare "to cut"
A line that intersects a curve or circle at two points
(See also Secant (sec) function in a right triangle - trigonometry).
Try this Drag either orange dot. The blue line will always remain a secant to the circle, except that if the two points coincide, the secant becomes a tangent.

The blue line in the figure above is called the "secant to the circle c".

As you move one of the points P,Q, the secant will change accordingly. If the two points coincide at the same point, the secant becomes a tangent, since it now touches the circle at just one point.

The line segment inside the circle between P and Q is called a chord.

Intersecting Secants

As shown in the figure on the right, when two secants intersect at a point outside the circle, there is an interesting relationship between the line segments thus formed.

See Intersecting Secants Theorem for a detailed explanation.

Other definitions

In trigonometry, the secant of an angle in a right triangle is the ratio of the hypotenuse to the adjacent side. The reciprocal of cosine. See Secant (sec) function in a right triangle - trigonometry.
While you are here..

... I have a small favor to ask. Over the years we have used advertising to support the site so it can remain free for everyone. However, advertising revenue is falling and I have always hated the ads. So, would you go to Patreon and become a patron of the site? When we reach the goal I will remove all advertising from the site.

It only takes a minute and any amount would be greatly appreciated. Thank you for considering it!   – John Page

Become a patron of the site at   patreon.com/mathopenref

Other circle topics

General

Equations of a circle

Angles in a circle

Arcs