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26 Jun 2022, 18:15
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
27% (01:34) correct
73%
(02:58)
wrong
based on 30
sessions
History
Date
Time
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Not Attempted Yet
In a circle of radius 5 units, CD and AB are perpendicular diameters. A chord CH cutting AB at K is 8 units long. The diameter AB is divided into two segments whose dimensions are:
A. 1.25, 8.75
B. 2.75, 7.25
C. 2, 8
D. 4, 6
E. None of these
Chinese GMAT Shuxue Nanti Jingjie
A. 1.25, 8.75
B. 2.75, 7.25
C. 2, 8
D. 4, 6
E. None of these
Chinese GMAT Shuxue Nanti Jingjie
17 Jul 2022, 09:21
Kudos
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Hello
Let the center be O
CHD is inscribed in the circle so CD is the hypothenuse.
I recognize 10²=8²+6² pattern
Now the Angle DCH = Angle OCK.
So we can apply the same 3:4:5 pattern to the triangle COK :
the second larger side of the triangle is CO (roughly saw on the drawing) so this one corresponds to the "4" above.
We have then 3x:4x:5x where x =5/4
Now solve for 3x= 3*5/4= 15/4=3,75
Therefore
OK=3,75
AK = AO + OK = 5+ 3,75 = 8,75
Answer A. Maybe there's a better and faster solution. Would be glad to read
Let the center be O
CHD is inscribed in the circle so CD is the hypothenuse.
I recognize 10²=8²+6² pattern
Now the Angle DCH = Angle OCK.
So we can apply the same 3:4:5 pattern to the triangle COK :
the second larger side of the triangle is CO (roughly saw on the drawing) so this one corresponds to the "4" above.
We have then 3x:4x:5x where x =5/4
Now solve for 3x= 3*5/4= 15/4=3,75
Therefore
OK=3,75
AK = AO + OK = 5+ 3,75 = 8,75
Answer A. Maybe there's a better and faster solution. Would be glad to read
27 Sep 2025, 07:05
Kudos
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We have CD=10 and CH=8 and angle(CHD)=90, as it is on the diameter
Therefore by PGT, HD=6
Now Tr(COK)~Tr(CHD)
CO/CH = OK/HD
5/8 = OK/6
OK = 3.75
AK = 5-3.75 = 1.25
Hence, the answer is A
twobagels
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