Question

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

Answer 1

4 units

Explanation:

just took the test

Answer 2

4 units

Explanation:

Chord theorem: The product of the lengths of the segments of one chord equals the product of the lengths of the segments of the other chord.

AC and DB are the chords.

AH * HC = DH * HB

(20 -x) *x = (x +4)*(12 - x)

Use distributive property.

20x - x² = x*12 - x*x + 4*12 - 4*x

20x - x² = 12x - x² + 48 -4x

20x - x² = 12x - 4x - x² + 48

Combine like terms in the RHS.

20x - x² = 8x - x² + 48

Add x² to both sides.

20x - x² + x² = 8x + 48

20x = 8x + 48

Subtract 8x from both sides.

20x - 8x = 48

12x = 48

Divide both sides by 8.

x = 48 ÷ 12

`\boxed{\bf x = 4 \ units}`