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15 Jul 2022, 08:00
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
75%
(hard)
Question Stats:
58% (02:30) correct
43%
(02:33)
wrong
based on 120
sessions
History
Date
Time
Result
Not Attempted Yet
Right angle ABC is inscribed in a quarter of a circle, as shown above. What is the length of line segment DC ?
A. 3
B. 4
C. 5
D. 7
E. 15
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Attachment:
2022.png
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15 Jul 2022, 09:24
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Answer choice is C
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IMG_20220715_215034.jpg [ 1.3 MiB | Viewed 4399 times ]
General Discussion
15 Jul 2022, 09:05
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Bunuel
Extend the figure to the right by drawing the other quarter of the circle and extending BC until it intersects with the circle at point E. AB is 24.
Starting with triangle ABE, we have right triangle with a side that looks like it'll make a tidy 3-4-5. Let's see if we can backdoor our way to the solution.
AB is 24 and is the shortest side of triangle ABE. If that is the "3" in a 3-4-5, the other leg will be 32 and the hypotenuse will be 40. The hypotenuse is 2r, so r=20. We are given that BC is 7, so that would make CE 25 and CO is 15. That makes DC = 5.
ABE and COE are similar and ABE is a 3-4-5, so COE should be, too. It is, so everything checks out.
Answer choice C.
