In the given figure, O is the center of the circle and BC is the tange

Question

https://gmatclub.com/forum/download/file.php?id=54929 In the given figure, O is the center of the circle and BC is the tangent. If AB = 10cm. What is the length of the tangent BC? (1) The product of the length of OB and AB is 170. (2) The circumference of the circle is 14π. Project DS Butler Data Sufficiency (DS3) For DS butler Questions Click Here 1.png

abhishekdadarwal2009 · Answer

IMO D,

Sol.
AB=10,
1.AB*OB=170 ie OB=17 and OA=7 and OC=7.
we know tangent always make 90degrees with center, so BC and CO are 90 thus triangle BCO is right triangle and we can find all sides with this info. Thus sufficient.
2.circum of circle-14pi so we know the radius =7. and we get OC and OA=7, same as first we can findout all the lenghts. Thus sufficient.

D is correct

GMATWhizTeam · Answer

Solution 
 Step 1: Analyse Question Stem 
 •  OC = OA =  radius of the circle (let’s say r)
•  AB = 10  cm
• BC is tangent so, triangle OCB is a right angled triangle.(as shown below)
  https://www.dropbox.com/s/u6it6fo3uy0cyo3/06_02_right.png?dl=1 
• We need to find the length of BC. 
 o Now, in triangle, OCB,
   BC^2 = OB^2 – OC^2 = ( r + 10)^2 – r^2    
Thus, to find BC we need to find r.

Step 2: Analyse Statements Independently (And eliminate options) – AD/BCE 
 Statement 1:  The product of the length of OB and AB is 170.
 •  OB*AB = (r+10)*10 = 170 ⟹ r + 10 = 17 ⟹ r = 7  
Hence, statement 1 is sufficient and we can eliminate answer Options B, C and E.

Statement 2:  The circumference of the circle is 14π.
•  2*\pi*r = 14\pi ⟹ r = 7 
Hence, statement 2 is also sufficient.
Thus, the correct answer is  Option D.

yashikaaggarwal · Answer

IMO D

Line drawn to tangent subtends 90°
OB^2=BC^2+OC^2 --------(1)

Statement 1: product of line OB*AB=170. (AB = 10)
OB= 170/10 => OB=17 -----(2)
OB=OA+AB => 17-10=0A => OA=7=OC
Putting values in equality (1)
17^2-7^2 = BC^2
289-49 = BC^2 
240 = BC^2
BC^2 = 2*2*2*2*3*5
BC = 4√15
{sufficient}

Statement 2: circumference of Circle = 14π = 2πr => r=7
OC=7 , OB=OA+AB = 7+10 = 17
Putting values in equality (1)
17^2-7^2 = BC^2
289-49 = BC^2 
240 = BC^2
BC^2 = 2*2*2*2*3*5
BC = 4√15
{sufficient}

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sambitspm · Answer

To solve the length of tangent BC, we need only radius.

Statement 1 => AB*OB = 170
AB is 10, so OB = 17 so we have radius
SUFFICIENT

Statement 2 => Circumference is known,
Radius is known
SUFFICIENT

D

hacorus · Answer

In the given figure, O is the center of the circle and BC is the tangent. If AB = 10cm. What is the length of the tangent BC?

What do we have:
 As a tangent is perpendicular to the circle, we know that OCB is rectangle in C.
And if we applied the theorem for rectangular triangles, we know that OB^2=OC^2+BC^2 or BC^2 = OB^2 - OC^2
OB=OA+AB and we already have AB=10cm

So what we are really looking for is the Radius of the circle, OC or OA (all 3 are equal)?

Let's start with (1) The product of the length of OB and AB is 170.
We know: OB=OA+AB and AB=10cm
OB*AB =170 = OB * 10 so OB = 17cm
OB=OA+AB or 17= OA + 10 so OA = 7cm = OC
We have everything, BC^2 = OB^2 - OC^2 = 17^2 + 7^2, no need to do the maths, only the positive value of BC is valid (lengths are positive), so (1) is sufficient and the answer is either A or D.

Let's take (2) The circumference of the circle is 14π.
Circumference of a circle is 2*pi*Radius
We have: 2*pi*R=14*pi so R=7cm = OC = OA
OB=OA+AB = 7+10=17cm
We have everything: BC^2 = OB^2 - OC^2 = 17^2 + 7^2, no need to do the maths, (2) is sufficient. So D

The correct answer is D

Batman117 · Answer

D.
Here angle ocb is 90

1.OB*AB=170
OB=OA+AB
So OA=10=OC=radius
So as per Pythagoras theorem
Oc^2+ob^2 =bc^2

Sufficient

2.2pi radius=14 pi
R=oc=oa

Sufficient

D.

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anupam87 · Answer

Angle OCB is 90 degrees. If we can find the radius of the circle we can find the length of BC.

Statement1 - we can find OA - Sufficient. 
Statement2 - we can find the radius - Sufficient.

Answer - D

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patrapan · Answer

Option A

as tangent is 90 to the radius so using Pytho theorem we can find the length of tangent

HoneyLemon · Answer

D   ,IMO

In the given figure, O is the center of the circle and BC is the tangent. If AB = 10cm. What is the length of the tangent BC?

In the triangle OBC , angle OCB is 90 (since BC is tangent ). Now to find the length of BC , we just need OB and OC. 
To get length of OB and OC , we need the radius of the circle. 
 
Basically the ques now reduced to , what is the length of the radius of the circle ?

(1) The product of the length of OB and AB is 170.
 OB . AB = 170 => OB = 17 => OA = 7 = radius .. Sufficient

(2) The circumference of the circle is 14π.

circumference goven . We can easily find radius . Sufficient

Hence D .

Shrey08 · Answer

D. Both the statement are sufficient.

AB =10; BC= ?

OCB forms a right angled triangle.

Statement 1 : OB*AB= 170

OB= 17
OB-AB= OA= 7
OA=OC 7 (Both are radius)
we know OC and OB
We can find BC using Pythagorean theorem.
 Sufficient

Statement 2 : The circumference of the circle is 14π.
say  d  is diameter and  r  is radius

dπ = 14π ; d = 14 ; r = 7

OC=OA = 7
OA+AB= OB = 17

We know OC and OB
we can find BC using pythagorean therom.
 Sufficient

In the given figure, O is the center of the circle and BC is the tange

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