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In the diagram above, line BC touches the circle at point C, and the

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Bunuel
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In the diagram above, line BC touches the circle at point C, and the [#permalink] New post   17 Jul 2016, 11:27
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In the diagram above, line BC touches the circle at point C, and the distance from B to C is 35 cm. What is the area of the circle?

(1) AB = 25 cm

(2) Angle OCB = 90°

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tangent-line-unknown-radius.jpg
tangent-line-unknown-radius.jpg [ 18.82 KiB | Viewed 3240 times ]
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gauravsaggis1
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Re: In the diagram above, line BC touches the circle at point C, and the [#permalink] New post   17 Jul 2016, 13:08
BC touches the circle at C. so, angle OCB= 90.
BC =35, OC = OA= radius of circle =r
from statement 1) AB =25
applying Pythagoras theorem in OCB.
OB^2= OC^2+ BC^2
can be solved for r=12 and then for area of circle (pi* r^2) can be calculated.
so, sufficient.
statement 2) gives the same information as is given in question stem. NOT sufficient.

ANS A.
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Re: In the diagram above, line BC touches the circle at point C, and the [#permalink] New post   17 Jul 2016, 16:50
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Anytime a line tangentially touches a circle we know that the angle of that line and the radius is 90º,
So immediately we know that answer choice B is useless as is provides no additional information.

So can we solve this with just answer choice A?
Essentially, we are looking for the area of a triangle. To solve this we need the Base and the Height (Radius and Length BC respectively)
We have the height = BC = 35
Answer choice A lets us find the radius, if we use the Pythagoras theorem: OB²= OC²+ BC²
or (r+25)² = 35² + r²

You don't even have to solve this any further, since we have one variable and one equation, it's clear just by looking at it that we could solve it with answer choice A alone.

Answer A
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Re: In the diagram above, line BC touches the circle at point C, and the [#permalink] New post   18 Jul 2016, 23:07
IMO: C
Reason why not A: We cannot assume that O in the figure is the center of the circle because the question does not mention it.
From (2), we then understand that Point O must be the center because the radius forms 90 degree to a tangent. Hence essentially, statement (2) says O is the center. Hence using (1) and (2), we can conclude that the answer must be C.


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In the diagram above, line BC touches the circle at point C, and the d [#permalink] New post   21 Jul 2016, 08:42
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Attachment:
tangent-line-unknown-radius.jpg
tangent-line-unknown-radius.jpg [ 18.82 KiB | Viewed 2851 times ]

In the diagram above, line BC touches the circle at point C, and the distance from B to C is 35 cm. What is the area of the circle?

Statement #1: AB = 25 cm

Statement #2: angle OCB = 90°

This GMAT DS practice question contains a tautological statement. In the logic of DS, there is a subtle but important difference in whether a statement is tautological vs. merely insufficient. For a discussion of this complex issue, as well as the OE of this particular question, see:
GMAT Data Sufficiency Logic: Tautological Statements

Mike :-)
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Re: In the diagram above, line BC touches the circle at point C, and the [#permalink] New post   21 Jul 2016, 09:36
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Ans Should be C as we are not given if O is the center unless we are told that the angle OCB is 90 which B does. hence together the statements are sufficient.
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Re: In the diagram above, line BC touches the circle at point C, and the [#permalink] New post   05 Aug 2020, 08:59
mikemcgarry wrote:
Attachment:
tangent-line-unknown-radius.jpg

In the diagram above, line BC touches the circle at point C, and the distance from B to C is 35 cm. What is the area of the circle?

Statement #1: AB = 25 cm

Statement #2: angle OCB = 90°

This GMAT DS practice question contains a tautological statement. In the logic of DS, there is a subtle but important difference in whether a statement is tautological vs. merely insufficient. For a discussion of this complex issue, as well as the OE of this particular question, see:
GMAT Data Sufficiency Logic: Tautological Statements

Mike :-)


Hi Mike,
Can you please clarify one doubt here? In geometry DS questions, when it is safe to assume the angle and when it's not. In this question, we have taken the angle as 90, so can I always take the angle as 90 if it's mentioned that line touches the circle at some point? https://gmatclub.com/forum/what-is-the- ... 75530.html In this link we didn't assume the angle to be 90 degree, but I did. How to avoid these kinds of mistakes? Kindly comment.
Thanks in advance
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gmatclubot
Re: In the diagram above, line BC touches the circle at point C, and the [#permalink]
05 Aug 2020, 08:59
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