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?

Answer 1

The answer is C on Edge 2020

Explanation:

I did the Exam

Answer 2

16 units

Explanation:

Chords AC and DB intersect at H and:

AH =20-x

HB=12-x

DH=x + 4

HC=x.

Using the theorem of intersecting chords

AH X HC = DH X HB

`x(20-x)=(x+4)(12-x)\\20x-x^2=12x-x^2+48-4x\\20x=8x+48\\20x-8x=48\\12x=48\\x=4`

Therefore:

DB = DH +HB

=x+4+12-x

=4+4+12-4

=16 Units