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Minor arc AB in the diagram is 30 and the radius of the circle is 6. Find the area of circular segment AB.

Feb 22, 2022

#1
+1384
+2

What diagram?

Feb 23, 2022
#2
+1

I couldn't attach it, but I think it's still possible to solve without it.

If you need the description, here it is:

It's a circle with center O and B and A are two points on the edge of the circle (B comes before A when clockwise).

Guest Feb 23, 2022
#3
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The area of the segment is 6*pi - 12.

Feb 23, 2022
#4
+1384
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Oh wait, never mind, I think I know how to solve it.

The circular segment is equal to the area of the region $$ABO-\triangle{ABO}$$

We know the circular region's area is $${30 \over360} \times 36\pi =3\pi$$

$$\triangle{ABO}$$ is isosceles, with degrees of 30, 70, 70, and 2 sides with 6. Using trig, we find that the area of the triangle is 9.

Thus, the area of the circular region is: $$\color{brown}\boxed{3\pi - 9}$$

Feb 24, 2022