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

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calculista calculista · Answer 1 · 2019-07-20T02:20:47+02:00

Answer:

[tex]MN=18\ units[/tex]

Step-by-step 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

[tex]AB*BD=MB*BN[/tex]

substitute

[tex](9)(x+1)=(x-1)(15)\\ \\9x+9=15x-15\\ \\15x-9x=9+15\\ \\ 6x=24\\ \\x=4\ units[/tex]

Find the length of line segment MN

[tex]MN=MB+BN=(x-1)+15=x+14[/tex]

substitute the value of x

[tex]MN=4+14=18\ units[/tex]

eudora eudora · Answer 2 · 2019-08-12T18:30:41+02:00

Answer:

MN = 18

Step-by-step 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.