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Source: — Data Sufficiency |
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by rijul007 » Mon Dec 26, 2011 9:58 pm
karthikpandian19 wrote:P is a circle with radius r. If AB is a chord in circle P, is AB<6?

(1) r=5

(2) The height from the center of P to AB is smaller than 4.
(1) r=5

The longest chord in a circle is it diameter

0 < AB < 10

Not sufficient


(2) The height from the center of P to AB is smaller than 4.


Image


a < 4
r = ?
length of AB depends on the value of both a and r

Insufficient


Combining (1) & (2)

r = 5
a < 4

for largest legth of AB,
a = 0
x = √25 = 5
AB = 2x = 10

smallest length of AB,
a = 3.99999999 = 4 approx
x = √(25 - 16) = 3
AB = 6

6 < AB < 10

This answers the ques "Is AB<6? " with a NO


Option C[/b]
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by arpan20690 » Tue Dec 27, 2011 12:43 am
I would like to Change the last part of rijul007's post i.e combining 1) and 2).
let AB = 2x
if we apply right angle formula for the triangle
then x^2 + a^2 = 5^2 ; a^2 = 25 - x^2
and also a^2 < 4^2.
so 25 - x^2 < 16
; x^2 > 9
; x > 3
AB = 2x > 6
So we can answer that AB is not less than 6. So, data SUFFICIENT.
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by karthikpandian19 » Tue Dec 27, 2011 9:29 pm
OA is C
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