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notsponge [240]
3 years ago
10

AC and DB are chords that intersect at point H.

Mathematics
2 answers:
valentinak56 [21]3 years ago
7 0

Answer:

16 units

Step-by-step explanation:

see the attached figure to better understand the problem

Applying  the Intersecting Chords Theorem

we have that

AH*HC=DH*HB

substitute the given values

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

20x-x^2=12x-x^2+48-4x

Simplify

20x=8x+48

20x-8x=48

12x=48

x=4

Find out the length of segment DB

DB=DH+HB

DB=(x+4)+(12-x)=16\ units

<em>Note</em> In this problem it was not necessary to determine the value of x to calculate the DB segment.

Anyway, the calculation was done for didactic purposes.

marusya05 [52]3 years ago
3 0

The length of line segment DB is 16 units

<h3>Explanation: </h3>

The Intersecting Chords Theorem or chord theorem states that when two chords are intersecting within a circle, the product of their respective segments is equal. This also a statement in elementary geometry that describes a relation of the four line segments created by two intersecting chords in a circle. It states that the products of the lengths of the line segments on each chord are equal.

AC and DB are chords that intersect at point H as shown in the figure below.

The intersection definition is, if the intersection happened of two sets A and B it is denoted by A ∩ B. It is the set  that contains all elements of A that also belong to B, and nothing else. An intersection is a single point where two lines meet or cross each other.

AH*HC=DH*HB\\ (20-x)*(x)=(x+4)*(12-x)\\ 20x-x^{2} =12x-x^{2} +48-4x\\ 20x-12x+4x=48\\ 12x=48\\ x=4

Then we should find the length of the segment DB . The line segment is a part of a line with two distinct end points.

DB=(x+4)+(12-x)\\ DB=(4+4)+(12-4)\\ DB=8+8\\ DB=16\ units

Therefore  the length of line segment DB is equal to  16 units

Learn more about the length   brainly.com/question/729447

#LearnWithBrainly

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