When two secant lines intersect each other outside a circle, the products of their segments are equal.

(Note: Each segment is measured from the outside point)

Try this
In the figure below, drag the orange dots around to reposition the secant lines.
You can see from the calculations that the two products are always the same.
(Note: Because the lengths are rounded to one decimal place for clarity, the calculations may come out slightly differently on your calculator.)

See also Intersecting Secant Angles Theorem.

This theorem works like this: If you have a point outside a circle and draw two secant lines (PAB, PCD) from it, there is a relationship between the line segments formed. Refer to the figure above. If you multiply the length of PA by the length of PB, you will get the same result as when you do the same thing to the other secant line.

More formally: When two secant lines AB and CD intersect outside the circle at a point P, then

PA.PB = PC.PD

It is important to get the line segments right. The four segments we are talking about here all start at P, and some overlap each other
along part of their length; PA overlaps PB, and PC overlaps PD.
PA^{2} = PC.PD

This is the Tangent-Secant Theorem.
PA^{2} = PC^{2}

By taking the square root of each side:
PA = PC

confirming that the two tangents froma point to a circle are always equal.
- 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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