# Segments Formed by a Tangent and a Secant

How to solve the segments formed by a tangent and a secant problems: formula, example, and its solution.

## Formula

[blue]^{2} = [green]⋅[dark green]

[blue]: Segment from the tangent

[green]: Exterior segment from the secant

[dark green]: The secant including [green]

## Example

The tangent segment is *x*.

The secant segments are 4 and 5.

So *x*^{2} = 4(4 + 5).

4 + 5 = 9

4⋅9 = 36

So *x*^{2} = 36.

Square root both sides.

Then *x* = √36*x* > 0

So you don't have to write (±)

in front of the square root sign.

36 = 6^{2}

Then cancel the square and the square root.

So *x* = 6.

Square root