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Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  In the figure above, O is the center of the circle. If AB has a length

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Math Expert V
Joined: 02 Sep 2009
Posts: 55803
In the figure above, O is the center of the circle. If AB has a length  [#permalink]

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Difficulty:   25% (medium)

Question Stats: 94% (01:23) correct 6% (01:43) wrong based on 24 sessions

HideShow timer Statistics  In the figure above, O is the center of the circle. If AB has a length of 16 and OB has a length of 10, what is the length of CD ?

A. 2

B. 4

C. $$2\sqrt{3}$$

D. $$8-\sqrt{35}$$

E. $$8-\sqrt{39}$$

Attachment: 2019-01-10_1419.png [ 16.83 KiB | Viewed 384 times ]

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Re: In the figure above, O is the center of the circle. If AB has a length  [#permalink]

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Bunuel wrote: In the figure above, O is the center of the circle. If AB has a length of 16 and OB has a length of 10, what is the length of CD ?

A. 2

B. 4

C. $$2\sqrt{3}$$

D. $$8-\sqrt{35}$$

E. $$8-\sqrt{39}$$

In right triangle OBD, BD = (1/2)*AB = 8, AB = 10

Attachment:
2019-01-10_1419.png

i.e. OD = 6 (Using pythagorean triplet 6-8-10)

CD = CO - OD = 10-6 = 4

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Intern  B
Joined: 10 Feb 2018
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GMAT 1: 550 Q46 V20 Re: In the figure above, O is the center of the circle. If AB has a length  [#permalink]

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my answer is option B ie 4
OBD being a right angled triangle with OB =10 and BD=8, we get OD=6.
Therefore, CD=10-6=4
e-GMAT Representative D
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Re: In the figure above, O is the center of the circle. If AB has a length  [#permalink]

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Solution

Given:
• O is the center of the circle
• AB = 16
• OB = 10

To find:
• The length of CD

Approach and Working:
OD bisects AB
• Thus, $$DB = \frac{AB}{2} = \frac{16}{2} = 8$$

In triangle ODB,
• $$OB^2 = OD^2 + DB^2$$
• Implies, $$100 = OD^2 + 64$$
• OD = 6

OC = radius = OD + CD
• CD = 10 – 6 = 4

Hence, the correct answer is Option B

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Re: In the figure above, O is the center of the circle. If AB has a length  [#permalink]

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[quote="Bunuel"] In the figure above, O is the center of the circle. If AB has a length of 16 and OB has a length of 10, what is the length of CD ?

A. 2

B. 4

C. $$2\sqrt{3}$$

D. $$8-\sqrt{35}$$

E. $$8-\sqrt{39}$$

oc=ob=oa=10
and od=6 triangle ado = 3:4:5 = 6:8:10
so dc= oc-od = 10-6 = 4
IMO B
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If you liked my solution then please give Kudos. Kudos encourage active discussions. Re: In the figure above, O is the center of the circle. If AB has a length   [#permalink] 10 Jan 2019, 07:42
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