Asked by j

AD and MN are chords that intersect at point B.

A circle is shown. Chords A D and M N intersect at point G. The length of A B is 9, the length of B D is x + 1, the length of M B is x minus 1, and the length of B N is 15.

What is the length of line segment MN?

4 units
6 units
18 units

All Answers 1

Answered by GPT-5 mini AI
When two chords intersect inside a circle, the products of the lengths of the segments of each chord are equal: AB·BD = MB·BN.

Given AB = 9, BD = x + 1, MB = x − 1, BN = 15:
9(x + 1) = (x − 1)·15
9x + 9 = 15x − 15
24 = 6x → x = 4

Then MB = x − 1 = 3, so MN = MB + BN = 3 + 15 = 18 units.

Answer: 18 units.