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655-705 (Hard)|   Geometry|      
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Bunuel
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In the diagram below, a rectangle ABCD is drawn inside a semicircle. 23 Jul 2017, 23:20
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C
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58% (02:10) correct 42% (02:21) wrong based on 127 sessions

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In the diagram below, a rectangle ABCD is drawn inside a semicircle. What is the length of AB?


(1) The radius of the semicircle is 10.
(2) AB : BD = 3 : 2

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Attachment:
2017-07-24_1020.png
2017-07-24_1020.png [ 5.09 KiB | Viewed 3855 times ]
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C
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In the diagram below, a rectangle ABCD is drawn inside a semicircle. 24 Jul 2017, 01:28
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Bunuel
In the diagram below, a rectangle ABCD is drawn inside a semicircle. What is the length of AB?


(1) The radius of the semicircle is 10.
(2) AB : BD = 3 : 2

Show Spoiler
Attachment:
2017-07-24_1020.png
Show more

(1) If we know the length of the radius of the semicircle, we could know the length of OA and OB. However, we can't know the length of AB. Insufficient.

(2) If AB : BD = 3 : 2, since AB = 2 * OD, we have OD : BD = 1.5 : 2 = 3 : 4.

In right triangle OBD, since we know the ratio of OD and BD, we could calculate the length of AB based on the length of OD. However, we can't know exactly what the length of OD is. So insufficient.

Combine (1) and (2): We could easily calculate the length of AB. Sufficient.

THe answer is C.
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In the diagram below, a rectangle ABCD is drawn inside a semicircle. 27 Apr 2018, 16:04
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broall
Bunuel
In the diagram below, a rectangle ABCD is drawn inside a semicircle. What is the length of AB?


(1) The radius of the semicircle is 10.
(2) AB : BD = 3 : 2

Show Spoiler
Attachment:
2017-07-24_1020.png

(1) If we know the length of the radius of the semicircle, we could know the length of OA and OB. However, we can't know the length of AB. Insufficient.

(2) If AB : BD = 3 : 2, since AB = 2 * OD, we have OD : BD = 1.5 : 2 = 3 : 4.

In right triangle OBD, since we know the ratio of OD and BD, we could calculate the length of AB based on the length of OD. However, we can't know exactly what the length of OD is. So insufficient.

Combine (1) and (2): We could easily calculate the length of AB. Sufficient.

THe answer is C.
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We have got the length of the OA from where we can use the notation of 1:√3:2 and find the length of the OC.Where the OC is midpoint of rectangle.From there AB can be determined.Please point out where i am getting me wrong.
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broall
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In the diagram below, a rectangle ABCD is drawn inside a semicircle. 27 Apr 2018, 20:49
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alphastallion
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Bunuel
In the diagram below, a rectangle ABCD is drawn inside a semicircle. What is the length of AB?


(1) The radius of the semicircle is 10.
(2) AB : BD = 3 : 2

Show Spoiler
Attachment:
2017-07-24_1020.png

(1) If we know the length of the radius of the semicircle, we could know the length of OA and OB. However, we can't know the length of AB. Insufficient.

(2) If AB : BD = 3 : 2, since AB = 2 * OD, we have OD : BD = 1.5 : 2 = 3 : 4.

In right triangle OBD, since we know the ratio of OD and BD, we could calculate the length of AB based on the length of OD. However, we can't know exactly what the length of OD is. So insufficient.

Combine (1) and (2): We could easily calculate the length of AB. Sufficient.

THe answer is C.

We have got the length of the OA from where we can use the notation of 1:√3:2 and find the length of the OC.Where the OC is midpoint of rectangle.From there AB can be determined.Please point out where i am getting me wrong.
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Sorry, but how do you come up with the highlighted?
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In the diagram below, a rectangle ABCD is drawn inside a semicircle. 28 Apr 2018, 04:13
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Sorry, but how do you come up with the highlighted?[/quote]

I have assumed the it as right angle triangle.so i got it ratio of sides as above..
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In the diagram below, a rectangle ABCD is drawn inside a semicircle. 28 Apr 2018, 04:18
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alphastallion

I have assumed the it as right angle triangle.so i got it ratio of sides as above..
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Which triangle is right triangle? I think your way is wrong.
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In the diagram below, a rectangle ABCD is drawn inside a semicircle. 08 May 2018, 04:59
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OD/BD = 3/4
OB = 5

pythagoras theorem.
OD^2+BD^2=OB^2=5^2=25
Hence OD can only be 3 (OD^2 = 9) and BD can only be 4 (BD^2 = 16).
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In the diagram below, a rectangle ABCD is drawn inside a semicircle. 13 Nov 2019, 09:04
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broall
Bunuel
In the diagram below, a rectangle ABCD is drawn inside a semicircle. What is the length of AB?


(1) The radius of the semicircle is 10.
(2) AB : BD = 3 : 2

Show Spoiler
Attachment:
2017-07-24_1020.png

(1) If we know the length of the radius of the semicircle, we could know the length of OA and OB. However, we can't know the length of AB. Insufficient.

(2) If AB : BD = 3 : 2, since AB = 2 * OD, we have OD : BD = 1.5 : 2 = 3 : 4.

In right triangle OBD, since we know the ratio of OD and BD, we could calculate the length of AB based on the length of OD. However, we can't know exactly what the length of OD is. So insufficient.

Combine (1) and (2): We could easily calculate the length of AB. Sufficient.

THe answer is C.
Show more

How did we arrive at AB = 2*OD?
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stne
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In the diagram below, a rectangle ABCD is drawn inside a semicircle. 14 Nov 2019, 03:25
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Novice90
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Bunuel
In the diagram below, a rectangle ABCD is drawn inside a semicircle. What is the length of AB?


(1) The radius of the semicircle is 10.
(2) AB : BD = 3 : 2

Show Spoiler
Attachment:
2017-07-24_1020.png

(1) If we know the length of the radius of the semicircle, we could know the length of OA and OB. However, we can't know the length of AB. Insufficient.

(2) If AB : BD = 3 : 2, since AB = 2 * OD, we have OD : BD = 1.5 : 2 = 3 : 4.

In right triangle OBD, since we know the ratio of OD and BD, we could calculate the length of AB based on the length of OD. However, we can't know exactly what the length of OD is. So insufficient.

Combine (1) and (2): We could easily calculate the length of AB. Sufficient.

THe answer is C.

How did we arrive at AB = 2*OD?
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Hi Novice90,
ABCD is a rectangle, hence Opposite sides AB and CD are equal , also OD =\(\frac{1}{2}\)AB
hence 2*OD= AB
Hope its clear.
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In the diagram below, a rectangle ABCD is drawn inside a semicircle. 29 Oct 2022, 23:11
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