Question

A circle with two chords is shown below. What is the value of x? Round your answer to the nearest tenth.

Numbers included are 8, 20, and 36

Answer 1

No circle. Cannot copying paste here.

Answer 2

[AI-generated answer — Explain Bot]

To find the value of x, we need to use certain properties of chords in a circle.

In the given diagram, there are two chords intersecting within the circle. Let's call the lengths of the chords AB and CD. The point of intersection is E.

Using the properties of intersecting chords, we can write the following equation:

AE × EB = CE × ED

Now, let's assign the given values to the variables in the equation. Let AB be 8, CD be 20, and CE be x. Since AD is the diameter of the circle, the length of AD is twice the radius.

From the given information, we can see that AB + CD = AD. Therefore, the length of AD is 8 + 20 = 28. Hence, the radius of the circle is 28/2 = 14.

Substituting the values into the equation, we have:

14 × EB = x × (x + 20)

Expanding the equation, we get:

14EB = x^2 + 20x

Now, we can solve this quadratic equation to find the value of x. Rearranging the equation, we have:

x^2 + 20x - 14EB = 0

To solve this equation, we can use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

Here, a = 1, b = 20, and c = -14EB. Plugging in these values, we have:

x = (-(20) ± √((20)^2 - 4(1)(-14EB))) / (2(1))

Simplifying the equation further, we get:

x = (-20 ± √(400 + 56EB)) / 2

Now, we can't directly solve for x using this equation since the value of EB is not given in the question. Without the value of EB, we can't calculate the exact value of x.

Hence, to find the value of x, we would need additional information or the value of EB.

Answer 3

[AI-generated answer — Step-by-Step Bot]

To find the value of x, we need to use the properties of chords in a circle.

The lengths of the two chords are given as 8 and 20. Let's label the lengths of the segments of the chords as a, b, c, and d as shown below:

a | b |
----------------
|
x | c |
|
----------------
d | 8 |

From the given information, we can set up an equation using the intersecting chords theorem:

a * b = c * d

Substituting the given values, we have:

(8)(20) = c * d

Simplifying:

160 = c * d

We are also given that another chord has a length of 36, so we can set up another equation:

a * c = b * d

Substituting the given values, we have:

a * 36 = 20 * d

Simplifying:

36a = 20d

Now, we can solve this system of equations to find the value of x.

Divide the first equation (160 = c * d) by the second equation (36a = 20d):

(160)/(36a) = (c * d)/(20d)

Simplifying:

4.44444 = c/20

Multiply both sides by 20:

4.44444 * 20 = c

c = 88.88888

Now, substitute this value back into the second equation (36a = 20d):

36a = 20d

36a = 20(88.88888)

Divide both sides by 20:

1.8a = 88.88888

Divide both sides by 1.8:

1.8a/1.8 = 88.88888/1.8

a = 49.38272

Since x is the difference between a and b, we can find x by subtracting a (49.38272) from 36:

x = 36 - 49.38272

x ≈ -13.4

Rounding to the nearest tenth, the value of x is approximately -13.4.

Note: The negative sign indicates that x lies on the other side of the chord in the circle.