Question

Circles unit geometry please help​

Answer 1

Answer: B) 10pi

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Explanation:

AB is a diameter of the circle with point O in the center. This makes angle AOB to be 180 degrees. Consequently, arc ADB makes up 180 degrees of a full 360 degree circle (ie it makes up half of the circle since 180/360 = 1/2)

We're told that arc ADB is 15pi units long. Since arc ADB makes up half the circle, the full circle must therefore be 2*15pi = 30pi. This is the circumference.

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We're also told that angle COB is 60 degrees. Let's find angle COA

(angleCOA) + (angleCOB) = 180

angleCOA = 180-(angleCOB)

angleCOA = 180-60

angleCOA = 120

Angle COA is 120 degrees

This makes up 120/360 = 1/3 of the full circle

So (1/3)*(circumference) = (1/3)*(30pi) = 10pi is the arc length of AC where we take the shorter path from A to C along the circle's edge.

Answer 2

Answer:

AC = 10π

Step-by-step explanation:

Consider arc ADB with length 15π

ADB = circumference of circle × fraction of circle , that is

2πr × $\frac{180}{360}$ = 15π

2πr × $\frac{1}{2}$ = 15π

πr = 15π ( divide both sides by π )

r = 15

∠ AOC = 180° - 60° = 120° ( adjacent angle to 60° )

Thus

AC = 2πr × $\frac{120}{360}$

     = 2π × 15 × $\frac{1}{3}$

     = 30π × $\frac{1}{3}$

     = 10π