Question

what is the length of DK.....the answer choices are A. 8.5 B. 7.0 C. 12.7 D. 3.5

Answer 1

Picture?

Answer 2

idk how to send you the pic..but its a circle and at the side of the circle is AK= 14 EK=17 B=7

Answer 3

Save it to your computer and use the Attach File button, or right click and copy image url then paste it here.

Answer 4

https://huberheightscs2359-whs-ccl.gradpoint.com/Resource/8056052,0/Assets/testitemimages/geometry_b/circles/mc072-1.jpg

Answer 5

the products of the segments are equal

Answer 6

im horrible at this.. I need you to explain it to me please

Answer 7

Do you see the "chord" BE ? It is divided into two parts (by point K)
what are the lengths of each part?

Answer 8

each part of what chords?

Answer 9

do you see BE ?

Answer 10

yes

Answer 11

do you see point K on BE ?

Answer 12

yes

Answer 13

so BE is divided into two segments by point K
what are the lengths of each of those segments?

Answer 14

BK is 7

Answer 15

and the other one?

Answer 16

idk be

Answer 17

you want the length fro K to E

Answer 18

*from

Answer 19

it's the same as the length from E to K

Answer 20

EK is 17

Answer 21

yes (and hopefully it's clear that KE is the same length)
now you have the two parts of chord BE
you need the product of the two lengths (that means multiply the two lengths)

Answer 22

so multiply ke and be together ?

Answer 23

ke and kb (not be)

Answer 24

so 17 and 17?

Answer 25

ke is 17
kb is 7

Answer 26

its 119

Answer 27

ok, now we do the other chord , chord AD
what is the length of each segment of chord AD ?

Answer 28

AK is 14

Answer 29

and what is the other segment?

Answer 30

it is what we have to find:
what is the length of DK..

I would call it length "x" (x for unknown)
now find the product of 14 and x
do you know how to write 14 times x?

Answer 31

yes

Answer 32

how do you write it ?

Answer 33

14x

Answer 34

and the idea is those two products are equal
in other words
14x = 119

Answer 35

to find x, divide both sides by 14
\[ \frac{14}{14}x = \frac{119}{14} \]

Answer 36

8.5

Answer 37

on the left side 14/14 is 1, so the left side is just x
yes, you get
x= 8.5

Answer 38

i got it now! thank you!!

Answer 39

If I were doing it I would write
\[ 14x= 7\cdot 17\]
then divide both sides by 14 to get
\[ x = \frac{7\cdot 17}{14} \]
I know 7/14 is 1/2 so this is
\[ x= \frac{17}{2} \]
and finally
x= 8.5