Question

The chords intersect at point U. What is the value of y?

Answer 1

Answer:

6 centimeters.

Step-by-step explanation:

For chords that intersect inside a circle, we have the intersecting chords theorem, which states that the product of both colinear segments are equal to the products of the intersecting colinear segments meaning that:

$Segment 1*segment2 =segment3*segment4$

So 12*4=8*x

We just have to clear x from the equation to get the value of X:

$Segment 1*segment2 =segment3*segment4\\12*4=8*x\\x=\frac{12*4}{8}\\ x=6$

So the segment Y measures 6 cm.

Answer 2

we know that

The intersecting chords theorem states that the products of the lengths of the line segments on each chord are equal

so

in this problem

$RU*UT=QU*US$

we have

$RU=12\ cm\\UT=4\ cm\\QU=8\ cm\\US=y\ cm$

substitute the values

$12*4=8*y$

$48=8*y$

$y=6\ cm$

therefore

the answer is

$y=6\ cm$