The image shows the construction of two tangent lines from a point outside the circle to the circle. given that drawing the tangent lines jp and kp is step 5 in the construction and the answer choices represent steps 1 through 4, which is step 1?
a) construct the perpendicular bisector of op.
b) draw a circle and a point outside the circle.
c) draw two arcs on the circumference of the circle.
d) draw line op, to join the center o to point p.

(Draw a circle and a point outside the circle.)

Step-by-step explanation:

Step 1: Draw a circle and a point outside the circle.

Step 2: Draw line OP, to join the center O to point P.

Step 3: Construct the perpendicular bisector of OP.

Step 4: Draw two arcs on the circumference of the circle.

Step 5: Draw tangent lines JP and KP.

Proof:

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.