Segments Formed by a Tangent and a Secant

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].

[blue]2 = [green]⋅[dark green]

[blue]: Segment from the tangent
[green]: Exterior segment from the secant
[dark green]: The secant including [green]

Example

Find the value of x. Tangent segment: x. Secant segments: 4, 5.

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