Solve for x.
A. 8
B. 4
C. 10
D. 7

D. 7

Step-by-step explanation:

Apply the secant-scant product theorem. Thus, based on the theorem, we have the following equation:

6(4 + 6) = 5(x + 5)

6(10) = 5x + 25

60 = 5x + 25

Subtract 30 from each side

60 - 25 = 5x + 25 - 30

35 = 5x

Divide both sides by 5

35/5 = 5x/5

7 = x

x = 7

x = central angle apc = measure of minor arc ac

the two angles x and 30 add to 180, so x+30 = 180 and x = 180-30 = 150. the measure of minor arc ac is 150 degrees.

what we need to do from here is find the circumference and then multiply it by x/360 since there are 360 degrees in a circle. in this case, x = 150, so x/360 = 150/360 = 15/36 = 5/12. the shortest distance along the curve from a to c is 5/12 of the distance around the entire circle (aka circumference)

c = circumference

c = pi*d

c = pi*24

c = 24pi

now multiply this by 5/12 to get

distance along minor arc ac = (5/12)*(circumference)

distance along minor arc ac = (5/12)*(24pi)

distance along minor arc ac = 10pi

the formula you can use is

l = (x/360)*pi*d

with

l = length of minor arc

x = central angle

d = diameter

which essentially is the steps we took though a bit differently.

i can answer this question sweetie!

step-by-step explanation: