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]

The tangent segment is x.
The secant segments are 4 and 5.

So x² = 4(4 + 5).

4 + 5 = 9

4⋅9 = 36

So x² = 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 = 6²

Then cancel the square and the square root.

So x = 6.

Square root