What is the length of minor arc AC?

[AAPL]

Equilateral triangle ABC is inscribed within a circle as shown above. If the circle has an area of 36Ï€, what is the length of minor arc AC?

A. 3Ï€

B. 4Ï€

C. 5Ï€

D. 6Ï€

E. 9Ï€

The OA is B.

Please, can any expert assist me with this PS question? I don't have it clear and I appreciate if any explain it for me. Thanks.

[gillissm11]

A=36
$$\pi$$

[EconomistGMATTutor]

Hello AAPL.

If the area of the circle is 36Ï€ then $$A=36\pi\ =\ 6^2\pi,$$ it implies that r=6.

By the other hand, as the triangle is equilateral then its angles are equal to 60º.

Using the theorem of inscribed angle we got that the central angle in the arc AC is equal to 120º.



So, the length of minor arc AC is equal to $$AC=r\cdot\theta=6\cdot120º=720º=4\pi.$$ So, the correct answer is B .

I hope this explanation may help you.