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?

4 units
6 units
18 units
24 units

Answer 1

Answer:

18 units

Step-by-step explanation:

Answer 2

Using the intersecting chords theorem, the length of line segment MN is: C. 18 units.

What is the Intersecting Chords Theorem?

The intersecting chords theorem states that, when two chords intersect, the product of the segments of one chord is equal to the product of the segments of the other chord.

Given:

• AB = 9
• BD = x + 1
• MB = x - 1
• BN = 15

Thus:

(MB)(BN) = (AB)(BD)

Substitute

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

15x - 15 = 9x + 9

15x - 9x = 15 + 9

6x = 24

x = 4

MN = x - 1 + 15

Plug in the value of x

MN = 4 - 1 + 15

MN = 18 units

Learn more about intersecting chords theorem on:

https://brainly.com/question/14391758