What Is a Secant?

How a secant differs from a chord

Secants appear in many theorem settings because they connect inside-the-circle geometry with outside-the-circle geometry. Once an external point is added, secant lengths and angle relationships become important.

This page keeps the line extension visible outside the circle so the distinction between secant and chord is clear from the drawing itself.

The easiest check is to count the crossings with the circumference. Two distinct crossings make the full object a secant. The finite part between those crossings is a chord, so the two words can describe related parts of one drawing without meaning the same thing.

• A secant is a line that passes through a circle at two points.
• A chord is the inside segment cut from a secant when the endpoints on the circle are used.
• If the two intersection points merge into one limiting contact point, the line becomes a tangent.
• Secant geometry often involves both the outside segment and the full through-the-circle relationship.

Where secants are used

• Use secants in circle theorems involving external points and segment products.
• Use them when comparing a cutting line with a tangent line in angle problems.
• Use them in diagrams where the line must be treated as infinite rather than as a bounded segment.

Secant checks to make

• Do not call the inner piece alone a secant when the theorem is about the entire line.
• Do not confuse a two-point intersection with a tangent's one-point contact.
• Do not ignore the portions of the secant that lie outside the circle if the problem labels them.