Nadine is constructing a line perpendicular to ke←→ . she has constructed the arcs as shown. what is the next step in her construction? use a straight edge to draw a line through d and m. use a straight edge to draw a line through m and e. use a straight edge to draw a line through m and k. the image shows a horizontal line with points k, d, and e from left to right. point d looks halfway between points k and e. an arc is shown at point k turning inwards towards point d. an arc is shown at point e turning inwards towards point d. above point d is point m. two arcs go through point m. one arc faces southwest towards point k and one points southeast towards point e.

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.

5.5

step-by-step explanation: