In the figure above, two security lights, L1 and L2, are located 100

Question

https://gmatclub.com/forum/download/file.php?id=51542 In the figure above, two security lights, L1 and L2, are located 100 feet apart. Each illuminates an area of radius 100 feet, and both are located 60 feet from a chain-link fence. What is the total length s of fence, in feet, illuminated by the two lights? (A) 260 (B) 240 (C) 220 (D) 200 (E) 180 Are You Up For the Challenge: 700 Level Questions 2cir.png

chetan2u · Accepted Answer

Join  L_1  and  L_2

Step I -  Take  L_1L_2EC . It is a parallelogram so  L_1L_2=EC=100 
 Step II -  Drop a perpendicular at D, so  	riangle {L_2DE}  is right angled triangle with two sides in ratio 60:100, so third side will be 80 as it is a 3:4:5 triangle, and BE=80+80=160.
 Step III -  Find overlap or BC.
 BE=BC+CE.....160=BC+100...BC=60

WE have to find AE. 
 AE=AB+BC+CE=100+100+60=260  OR
AE=2*160-overlap=2*160-60=260

A

TestPrepUnlimited · Answer

The radius is 100 since their distance apart = radius = 100 ft. The distance of 60 ft represents the perpendicular length from the fence to any of the centers. So we can confirm each circle illuminates 80 * 2 = 160 ft of the fence using the 60 - 80 - 100 triangle. Finally, we need to subtract the overlap from the two fences. Note however the overlap cannot be more than 80, so the total fence length must be more than 160 + 160 - 80 = 240. We can only choose A.

Attachment:

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Archit3110 · Answer

TestPrepUnlimited 
see highlighted part ; option B is 240

chetan2u · Answer

At least 240 means answer can be 240 or 260?? So A or B possible

unraveled · Answer

Archit3110 Only possibility exists is A, since B would mean one circle passing through point of intersection of perpendicular from fence(chord) to center of other circle(L1 or L2). This would gravely deform the diagram. On the other side, if you are good at drawing circles to scale, you can observe that in the 60 - 80 - 100 triangle for L1 the perimeter of circle with center L2 bisects the side 80 in roughly a ratio of 1:3. Thus the common part of fence ~ \frac{3}{4} * 80 = 60 . Trying to quote 'Ron'

Hence A.

TestPrepUnlimited · Answer

Thank you for pointing that out, I have fixed my wording. The intent was to avoid doing any other calculations by seeing the overlap is certainly less than 80, so the fence length > 240.

freedom128 · Answer

The length of the fence covered by the light is: S = 80+100+80=260 feet.

Answer is (A)

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Shubhbansal698 · Answer

Please help me understand the question

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In the figure above, two security lights, L1 and L2, are located 100

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In the figure above, two security lights, L1 and L2, are located 100

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