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

The chords ac and db are intersecting chords, and the length of line segment db is 16 units

How to determine the length of segment db?

The given parameters are:

ah = 20 - x

hb = 12 - x

dh = x + 4

hc = x

Start by calculating the value of x using the following intersection chord equation

ah * hc = dh * hb

So, we have:

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

Solve for x

x = 4

The length of segment db is calculated using:

db = dh + hb

So, we have:

db = x + 4 + 12 - x

Substitute 4 for x

db = 4 + 4 + 12 - 4

Evaluate

db = 16

Hence, the length of line segment db is 16 units

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