Question

AD and MN are chords that intersect at point B what is the length of line segment MN?

Answer 1

MN = 18

Explanation:

AD and MN are two chords intersecting inside the circle at point B.

As we know from intersecting chords theorem.

AB × BD = BN × BM

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

9x + 9 = 15x - 15

15x - 9x = 15 + 9

6x = 24

x = 4

and MN = (x-1) + 15

= (x + 14)

= 4 + 14 ( By putting x = 4 )

= (18)

Therefore, MN = 18 is the answer.

Answer 2

`MN=18\ units`

Explanation:

we know that

The Intersecting Chord Theorem, states that When two chords intersect each other inside a circle, the products of their segments are equal.

so

In this problem

`AB*BD=MB*BN`

substitute

`(9)(x+1)=(x-1)(15)\\ \\9x+9=15x-15\\ \\15x-9x=9+15\\ \\ 6x=24\\ \\x=4\ units`

Find the length of line segment MN

`MN=MB+BN=(x-1)+15=x+14`

substitute the value of x

`MN=4+14=18\ units`