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14 Sep 2018, 01:54
Kudos
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
85%
(hard)
Question Stats:
44% (02:55) correct
56%
(02:36)
wrong
based on 32
sessions
History
Date
Time
Result
Not Attempted Yet
If A and B are tangent to the circle with center O as shown in the figure above, and AD has a length of 5 and AC has a length of 13, what is the radius of the circle?
A. 25/12
B. 65/12
C. \(\sqrt{34}\)
D. \(\sqrt{41}\)
E. \(\sqrt{50}\)
Attachment:
image036.jpg [ 2.86 KiB | Viewed 3466 times ]
14 Sep 2018, 02:11
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Bunuel
Triangle ADC is a right angle triangle with AC = 13 and AD = 5 i.e. CD = 12
Triangles ACD and OAD are similar triangle as per the property derived in attachment
hence,
AD / CD = OA / AC
OA = Radius = (5/12)*13 = 65/12
Answer: option B
Attachments
File comment: www.GMATinsight.com
Geometry 7 Similar Triangle Latest.jpg [ 195.88 KiB | Viewed 3247 times ]
10 Feb 2022, 08:28
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Hi,
definetly not easy, especially if one doesn't know about the alternate angle theorem. But applying the AAT, we can get the drawing below and the solution:
definetly not easy, especially if one doesn't know about the alternate angle theorem. But applying the AAT, we can get the drawing below and the solution:
Attachments
IMG_20220210_162619.JPG [ 3.58 MiB | Viewed 2557 times ]
05 Apr 2022, 08:19
Kudos
Bookmarks
One more way of solving could be to compare the area of the AOC obtained as follows-
Area of AOC = AD*OC = AC*OA
Put AC = 13, AD = 5 and OC = (13^2 - OA^2)^1/2. upon solving you find OA = 65/12.
Posted from my mobile device
Area of AOC = AD*OC = AC*OA
Put AC = 13, AD = 5 and OC = (13^2 - OA^2)^1/2. upon solving you find OA = 65/12.
Posted from my mobile device
