Two identical circles of area 144π are shown above. If the distance

Question

https://gmatclub.com/forum/download/file.php?id=39734 Two identical circles of area 144π are shown above. If the distance from point A to point B is 12, what is the perimeter of the shaded region? A. 4π B. 6π C. 8π D. 12π E. 24π image008.jpg

Sasindran · Answer

C.

Let the centre of the two triangles be O and P
Area=144π. r^2=144.
Solving for area we get the radius of each circle as 12. Also AB=12. Hence triangle OAB and PAB are equilateral triangles with side 12.

Hence Angle AOB=APB=60deg. Hence arc length of AB=2πr*60/360 = 2π*12/6=4π. Hence two arc length=2*4π =8π

karthikkaushik91 · Answer

It says area of two identical circles to be 144pie nt one circle alone.

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generis · Answer

image008ed.png Perimeter of the shaded region = arc length AB * 2 (i.e., not chord AB) Identical circles have identical circumferences Arc length = fraction of circumference To find that fraction, we need the central angle for the sector whose arc is AB (A sector's arc length is that portion of the circumference subtended by sector's central angle.) 1) Sector with arc AB? Draw a triangle in one of the circles Draw two lines, from center O to A, and from O to B. OA and OB are radii 2) Side lengths OA and OB of ∆ OAB = radius length Derive radius from area: 144π = πr^2 r^2 = 144 , r = 12 3) ∆ OAB is equilateral; all sides have equal length AB = OA = OB = 12, hence All angles of ∆ OAB = 60° Central angle of of sector AOB = 60° 3) Sector AOB as a fraction of the circle? \frac{Part}{Whole}=\frac{SectorAngle}{360}=\frac{60}{360}=\frac{1}{6} 4) Length of arc AB? \frac{1}{6} of circumference Circle's circumference, r = 12: = 2πr = (2π * 12) = 24π Arc Length: (\frac{1}{6} * 24π) = 4π 5) Perimeter of shaded region: (2 * length of arc AB) = (2 * 4π) = 8π Answer C

Two identical circles of area 144π are shown above. If the distance

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Two identical circles of area 144π are shown above. If the distance

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