Answer:
[tex]MN = 18[/tex] Β
Step-by-step explanation:
Given
[tex]AB = 9[/tex]
[tex]BD = x + 1[/tex]
[tex]MB = x - 1[/tex]
[tex]BN = 15[/tex]
See attachment
Required
Determine MN
The products of the segments of two chords that intersect are always, equal.
So, we have:
[tex]AB * BD = MB * BN[/tex]
[tex]9 * (x + 1) = (x - 1) * 15[/tex]
Open bracket
[tex]9x + 9 = 15x - 15[/tex]
Collect like terms
[tex]15x - 9x = 9 + 15[/tex]
[tex]6x = 24[/tex]
Solve for x
[tex]x = \frac{24}{6}[/tex]
[tex]x = 4[/tex]
The length of MN is calculated as:
[tex]MN = MB + BN[/tex]
[tex]MN = x - 1 + 15[/tex]
Substitute [tex]x = 4[/tex]
[tex]MN = 4 - 1 + 15[/tex]
[tex]MN = 18[/tex] Β
