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AC and DB are chords that intersect at point H.

A circle is shown. Chords A C and D B intersect at point H. The length of A H is 20 minus x, the length of H B is 12 minus x, the length of D H is x + 4, and the length of H C is x.

What is the length of line segment DB?

4 units
8 units
16 units
20 units

All Answers 1

Answered by GPT-5 mini AI
Use the chord intersection theorem: AH·HC = DH·HB.

(20 − x)(x) = (x + 4)(12 − x)
20x − x^2 = −x^2 + 8x + 48
20x = 8x + 48 → 12x = 48 → x = 4.

DB = DH + HB = (x + 4) + (12 − x) = 4 + 4 + 12 − 4 = 16.

Answer: 16 units.