When two chords intersect each other inside a circle, the products of their segments are equal.

It is a little easier to see this in the diagram on the right. Each chord is cut into two segments at the point of where they intersect. One chord is cut into two line segments A and B. The other into the segments C and D.

This theorem states that A×B is always equal to C×D no matter where the chords are.

In the figure below, drag the orange dots around to reposition the chords. As long as they intersect inside the circle, you can see from the calculations that the theorem is always true. The two products are always the same.

(**Note:** Because the lengths are rounded off for clarity, the calculations
will be slightly off if you enter the displayed values into your calculator).

When making doors or windows with curved tops we need to find the radius of the arch so we can lay them out with compasses. See Radius of an Arc for a way to do this using the Intersecting Chords Theorem.

- Circle definition
- Radius of a circle
- Diameter of a circle
- Circumference of a circle
- Parts of a circle (diagram)
- Semicircle definition
- Tangent
- Secant
- Chord
- Intersecting chords theorem
- Intersecting secant lengths theorem
- Intersecting secant angles theorem
- Area of a circle
- Concentric circles
- Annulus
- Area of an annulus
- Sector of a circle
- Area of a circle sector
- Segment of a circle
- Area of a circle segment (given central angle)
- Area of a circle segment (given segment height)

- Basic Equation of a Circle (Center at origin)
- General Equation of a Circle (Center anywhere)
- Parametric Equation of a Circle

- Arc
- Arc length
- Arc angle measure
- Adjacent arcs
- Major/minor arcs
- Intercepted Arc
- Sector of a circle
- Radius of an arc or segment, given height/width
- Sagitta - height of an arc or segment

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