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3 years ago

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

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Choice A

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In terms of "algebra", you can think
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Choice B

If we had a parallelogram with perpendicular diagonals, then we can prove that we have a rhombus (all four sides congruent). However, we don't know anything about the four angles of this parallelogram. Are they congruent? We don't know. So we can't prove this figure is a rectangle. The best we can say is that it's a rhombus. It may or may not be a rectangle. There isn't enough info about the rectangle & square part.

This is why choice B is the answer. We have some info, but not enough to be guaranteed everytime.

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Choice C

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Choice D

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Answer:

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Step-by-step explanation:

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