Answer:
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