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Updated on: 29 Dec 2019, 03:36
Originally posted by Sajjad1994 on 22 Jul 2019, 06:21.
Last edited by Sajjad1994 on 29 Dec 2019, 03:36, edited 2 times in total.
Last edited by Sajjad1994 on 29 Dec 2019, 03:36, edited 2 times in total.
Edited the question.
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In the figure, A and B are centers of two circles touching each other. The ratio of the radii of the two circles is 2 : 3, respectively. The two circles also touch a bigger circle of radius 9 internally as shown. If OB = 6, then AB =
(A) 10/3
(B) 13/3
(C) 5
(D) 13/2
(E) 15/2
Source: Nova GMAT
Attachment:
bhvg.jpg [ 21.27 KiB | Viewed 3717 times ]
23 Jul 2019, 05:07
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Let the radii of the two circles be 2k and 3k respectively. It’s given that the radius of the bigger circle is 9 units.
23rd July 2019 - Reply 3.jpg [ 14.16 KiB | Viewed 3444 times ]
As shown in the diagram, OC + CB + BD = 9. Also, OB = 6. This is possible only when CB = OC = 3.
This means that the radii are 3 units and 2 units respectively. AB is the distance between the centres of the two circles. Therefore, AB = 5 units.
The correct answer option is C.
An alternative approach would be to take the distance AB = 5k, since 2k and 3k are the respective radii of the circles.
Choosing option C, we can say 5k = 5, which will give us the radii as 2 and 3 respectively. This also satisfies the conditions that OB = 6 and the radius of the bigger circle = 9.
Choosing option D, we can say 5k = \(\frac{13}{2}\) which means k = \(\frac{13}{10}\) = 1.3. Therefore, the two radii are 3.9 and 2.6. But, 3.9 + 3.9 + 2.1 ≠ 9.
In a similar manner, you will be able to see that options A, B and E will give similar results and therefore, option C has to be the answer.
Hope this helps!
Attachment:
23rd July 2019 - Reply 3.jpg [ 14.16 KiB | Viewed 3444 times ]
As shown in the diagram, OC + CB + BD = 9. Also, OB = 6. This is possible only when CB = OC = 3.
This means that the radii are 3 units and 2 units respectively. AB is the distance between the centres of the two circles. Therefore, AB = 5 units.
The correct answer option is C.
An alternative approach would be to take the distance AB = 5k, since 2k and 3k are the respective radii of the circles.
Choosing option C, we can say 5k = 5, which will give us the radii as 2 and 3 respectively. This also satisfies the conditions that OB = 6 and the radius of the bigger circle = 9.
Choosing option D, we can say 5k = \(\frac{13}{2}\) which means k = \(\frac{13}{10}\) = 1.3. Therefore, the two radii are 3.9 and 2.6. But, 3.9 + 3.9 + 2.1 ≠ 9.
In a similar manner, you will be able to see that options A, B and E will give similar results and therefore, option C has to be the answer.
Hope this helps!
23 Jul 2019, 05:09
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Answer: C
Approach:
R = radius of outer circle
OB = 6
radius of circles A & B: 2x and 3x
R = OB + 3x
9 = 6 + 3x => x=1
AB = 2x + 3x => 2(1) +3(1)= 5
Hope it helps!
Approach:
R = radius of outer circle
OB = 6
radius of circles A & B: 2x and 3x
R = OB + 3x
9 = 6 + 3x => x=1
AB = 2x + 3x => 2(1) +3(1)= 5
Hope it helps!
