Question

Find the value of x

Answer 1

When chords intersect inside a circle, the chord segements are related by this expression:
\(ab = cd \)

Answer 2

sooo

Answer 3

Use the segments you are given and then set the product of the segements of one chord equal to the product of the segements of the other chord.

Answer 4

idk how

Answer 5

Do you know what the word product means? What is the product of 5 and 10?

Answer 6

5*10

Answer 7

Good. In math, product means a multiplication.
In this problem, you have a circle with two chords drawn.
The chords intersect inside the circle.
Ok so far?

Answer 8

yup

Answer 9

Good.
Because the chords intersect each other at a point, that point creates two parts for each chord. Each part of of each chord is called a segment of the chord.

Answer 10

The chord with numbers shown above has two segments. The length of one segment of the chord is 10. The length of the other segment is x.

Answer 11

yes

Answer 12

The other chord also has two segments. One has length of 15, and the other segment has length 5.

Answer 13

i see tht

Answer 14

Good.
What we know about these chords is:
The product of the lenghts of the segments of one chord equals the product of the lenghs of the segments of the other chord.

Remember, product is multiplication.

Multiply the lengths of the segments of one chord: 10x
Multiply the lengths of the segments of the other chord: 15 * 5

These products are equal, so:

10x = 15 * 5
Now we solve for x.

Answer 15

75

Answer 16

10x = 75
Divide both sides by 10:
x = 7.5