Question

AD and MN are chords that intersect at point B.

A circle is shown. Chords A D and M N intersect at point G. The length of A B is 9, the length of B D is x + 1, the length of M B is x minus 1, and the length of B N is 15.


What is the length of line segment MN?

Answer 1

C. 18 units

Explanation:

Answer 2

`MN = 18`

Explanation:

Given

`AB = 9`

`BD = x + 1`

`MB = x - 1`

`BN = 15`

See attachment

Required

Determine MN

The products of the segments of two chords that intersect are always, equal.

So, we have:

`AB * BD = MB * BN`

`9 * (x + 1) = (x - 1) * 15`

Open bracket

`9x + 9 = 15x - 15`

Collect like terms

`15x - 9x = 9 + 15`

`6x = 24`

Solve for x

`x = (24)/(6)`

`x = 4`

The length of MN is calculated as:

`MN = MB + BN`

`MN = x - 1 + 15`

Substitute
`x = 4`

`MN = 4 - 1 + 15`

`MN = 18`