The circle passes through (0, 6) and (0, – 6). Therefore, if we draw a chord between these two points, the length of the chord will be 12.

Again, the radius is 12. So if we connect the center and (0, 6) and (0, – 6), we get an equilateral triangle which has sides of length 12. Hence the angle created at the center by the chord is 60.
So, the area OAB = π(12)^2 * 60/360 = π*12*12*(1/6) = π*12*2 = 24π.

Now, the area of the triangle = (\sqrt{3} /4)*12*12 = \sqrt{3}*3*12 = 36\sqrt{3}.

So, the area of the of the part of this circle in the first quadrant = 1/2(24π - 36\sqrt{3}) = (12π - 18\sqrt{3})


Cheers.

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Dear saswata4s,

Thank you very much for finding this typo. You are 100% correct. I corrected the answer choices above.

Thanks again,
Mike McGarry
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in last wy are we myltiplyin by 1/2

Question is asking us for area in first quadrant only. Since area enclosed by in first quandrant = area enclosed in second quadrant we are dividing the total area by 2, hope this is clear