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What is the value of b? (1) The radius of the circle is 6 (2) ac = 12

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Bunuel
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What is the value of b? (1) The radius of the circle is 6 (2) ac = 12 [#permalink] New post   09 Sep 2018, 08:03
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44% (01:53) correct 56% (02:03) wrong based on 62 sessions
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What is the value of b?

(1) The radius of the circle is 6.
(2) ac = 12


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E
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rajudantuluri
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Re: What is the value of b? (1) The radius of the circle is 6 (2) ac = 12 [#permalink] New post   10 Sep 2018, 12:47
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PQ=a^2+b^2
QR=b^2+c^2

Because PQR is a right angled triangle, we have PQ^2+QR^2=PR^2.

(a^2+b^2)+(b^2+c^2)=(a+c)^2
(a^2+2*b^2+c^2)=a^2+c^2+2ac
2b^2=2ac
b^2=ac
b=sq.root of ac=sq.root of 12.

Hi Bunuel, shouldn't the answer be B?
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richa2909
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Re: What is the value of b? (1) The radius of the circle is 6 (2) ac = 12 [#permalink] New post   23 Sep 2018, 15:33
Hi rajudantuluri,
It is not mentioned anywhere that PR is the diameter of the circle, so you can not assume that PQR is a right angled triangle.
The answer is E.
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madhankumar666
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Re: What is the value of b? (1) The radius of the circle is 6 (2) ac = 12 [#permalink] New post   23 Sep 2018, 19:28
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richa2909 wrote:
Hi rajudantuluri,
It is not mentioned anywhere that PR is the diameter of the circle, so you can not assume that PQR is a right angled triangle.
The answer is E.

the two point P and R lies on the surface of the circle and the line PR passes through the radius then PR should be the diameter (in my opinion).
Take perpendicular bisector as T in the diagram. Take angle PRQ as X. Since triangle PQT is similar to triangle PQR.
b/c=(a+c)/b..
i.e., b^2=c(a+c).
the answer choice 1)provide a+C=12. but the value of c or a cannot be found .so , it is insufficient
2)ac=12 but the value of c or a cannot be found .so , it is insufficient.
combining two equation also does not provide solution. so answer is E
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Re: What is the value of b? (1) The radius of the circle is 6 (2) ac = 12 [#permalink]
23 Sep 2018, 19:28
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Bunuel
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