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26 May 2019, 02:52
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Difficulty:
45%
(medium)
Question Stats:
59% (01:37) correct
41%
(01:48)
wrong
based on 102
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The figure above represents a circular window with centre C. How long would a horizontal curtain rod have to be to span the window 8 inches directly above point c?
(1) A curtain rod that crosses the window 12 inches above C is 32 inches long
(2) The window has a radius of 20 inches
Attachment:
2019-05-26_1350.png [ 9.53 KiB | Viewed 7243 times ]
firas92
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26 May 2019, 03:04
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When the curtain rod is 8 inches above the centre, and lines are drawn from centre to ends of the rod, we will have 2 congruent right angled triangles, each with height 8 inches whose hypotenuse is equal to the radius of the circle and base, half the length of the curtain rod.
So if we know the radius, we can use pythagoras to calculate the length of the rod.
So essentially, we just need to know if we can calculate the radius of the circle.
Statement (1) gives us the length of the rod when height is 12 inches from centre. Using this length and height, we can calculate the radius of the circle.
(1) is sufficient
Statement (2) directly gives us the radius of the circle
(2) is sufficient
IMO, Answer is (D)
Hit Kudos if this helped!
So if we know the radius, we can use pythagoras to calculate the length of the rod.
So essentially, we just need to know if we can calculate the radius of the circle.
Statement (1) gives us the length of the rod when height is 12 inches from centre. Using this length and height, we can calculate the radius of the circle.
(1) is sufficient
Statement (2) directly gives us the radius of the circle
(2) is sufficient
IMO, Answer is (D)
Hit Kudos if this helped!
RupamPaul13
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26 May 2019, 03:22
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Statement 1:
given the length of a chord is 32 inches when perpendicular distance from the centre is 12 inches.
Length of a chord=2*sqrt(r^2-d^2) ; r=radius & d=perpendicular distance from the centre.
32=2*sqrt(r^2-10^2) from this we can get the value of r and thereby calculate the distance of the chord whose perpendicular distance from the centre is 8 inches: Statement 1 is sufficient.
Statement 2:
As stated earlier we have r=20 and d=8 so length of the chord can be determined and statement 2 is sufficient.
IMO Option D
given the length of a chord is 32 inches when perpendicular distance from the centre is 12 inches.
Length of a chord=2*sqrt(r^2-d^2) ; r=radius & d=perpendicular distance from the centre.
32=2*sqrt(r^2-10^2) from this we can get the value of r and thereby calculate the distance of the chord whose perpendicular distance from the centre is 8 inches: Statement 1 is sufficient.
Statement 2:
As stated earlier we have r=20 and d=8 so length of the chord can be determined and statement 2 is sufficient.
IMO Option D
