# Segments Formed by Two Intersecting Chords

How to solve the segments formed by two intersecting chords problems: formula, examples, and their solutions.

## Formula

[blue]⋅[dark blue] = [green]⋅[dark green]

[blue], [dark blue]: Segments from a chord

[green], [dark green]: Segments from the other chord

## Example 1

Four segments are formed

by two intersecting chords.

The segments are [*x*, 4] and [3, 8].

So *x*⋅4 = 3⋅8.

Divide both sides by 4.

Then *x* = 3⋅2.

3⋅2 = 6

So *x* = 6.

## Example 2

Previously, you've solved this problem.

Chord of a circle - Example

Let's solve the same example

by using the formula you've just learned.

To use the formula,

make the other chord.

The radius is 5.

And *OP* = 3.

So the green segment is, 5 - 3, 2.

Recall that

if a segment starts from the radius

and is perpendicular to the chord,

then the segment bisects the chord.

Chord of a circle*OP* is perpendicular to *AB*,

which is the chord of the given circle.

So *OP* bisects *AB*.

So set *AP* = *PB* = *x*.

Four segments are formed

by two intersecting chords.

The segments are [*x*, *x*] and [2, 8].

So *x*⋅*x* = 2⋅8.

*x*⋅*x* = *x*^{2}

2⋅8 = 16

Square root both sides.

Then *x* = √16*x* > 0

So you don't have to write (±)

in front of the square root sign.

16 = 4^{2}

Then cancel the square and the square root.

Then √4^{2} = 4.

Square root

*AB* = 2*x**x* = 4

So *AB* = 2⋅4.

2⋅4 = 8

So *AB* = 8.

As you can see,

you can get the same answer.