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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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Math Expert
Joined: 02 Sep 2009
Posts: 52108
What is the value of b? (1) The radius of the circle is 6 (2) ac = 12  [#permalink]

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09 Sep 2018, 07:03
00:00

Difficulty:

85% (hard)

Question Stats:

46% (01:38) correct 54% (01:51) wrong based on 52 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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image009.jpg [ 4.47 KiB | Viewed 731 times ]

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Re: What is the value of b? (1) The radius of the circle is 6 (2) ac = 12  [#permalink]

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10 Sep 2018, 11:47
1
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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Joined: 09 May 2017
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Re: What is the value of b? (1) The radius of the circle is 6 (2) ac = 12  [#permalink]

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23 Sep 2018, 14:33
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.
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Re: What is the value of b? (1) The radius of the circle is 6 (2) ac = 12  [#permalink]

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23 Sep 2018, 18:28
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 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 &nbs [#permalink] 23 Sep 2018, 18:28
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