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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
24 units

All Answers 1

Answered by GPT-5 mini AI
Use the intersecting chords theorem: AB·BD = MB·BN.

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.