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


I know the answer is 18 units but how did it get there I get 4 units

AD and MN are chords that intersect at point B. What is the length of line segment MN? I know the answer is 18 units but how did it get there I get 4 units class=

Verified Answer :

wolf1728

When 2 chords intersect in a circle, the product of their segments are equal.

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

9x +9 = 15x -15

24 = 6x

x = 4
SO,
Line AD = 9 + x + 1
Line AD = 14

Line MN = 15 + x -1
Line MN = 18


calculista

we know that

When two chords intersect each other inside a circle, the products of their segments are equal (Intersecting Chord Theorem)

so

In this problem

Step \(1\)

Find the value of x

\(AB*BD=MB*BN\\ 9*(x+1)=(x-1)*15\\ 9x+9=15x-15\\ 15x-9x=9+15\\ 6x=24\\ x=24/6\\ x=4\)

Step \(2\)

Find the value of MN

we know that

\(MN=MB+BN\\ MN=(x-1)+15\\ MN=(4-1)+15\\ MN=3+15\\ MN=18\)

therefore

the answer is

the length of line segment MN is \(18 units\)