ad and mn are chords that intersect at point b. what is the length of line segment mn? 4 units 6 units 18…

Explanation:

Step1: Apply the intersecting - chords theorem

When two chords (AD) and (MN) intersect at a point (B) inside a circle, the product of the lengths of the segments of one chord is equal to the product of the lengths of the segments of the other chord. So, (AB\times BD=MB\times BN). Here, (AB = 9), (BD=x + 1), (MB=x - 1), and (BN = 15). Then (9\times(x + 1)=(x - 1)\times15).

Step2: Expand the equation

Expand both sides: (9x+9 = 15x-15).

Step3: Solve for (x)

Move the (x) - terms to one side and the constants to the other side: (15 + 9=15x-9x). So, (24 = 6x), and (x = 4).

Step4: Find the length of (MN)

(MN=MB + BN=(x - 1)+15). Substitute (x = 4) into the equation: (MN=(4 - 1)+15=3 + 15=18) units.

Answer:

18 units