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

Question

https://gmatclub.com/forum/download/file.php?id=30999 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° tangent-line-unknown-radius.jpg

gauravsaggis1 · Answer

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.

mromrell · Answer

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

royrijit1 · Answer

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.

Sent from my iPhone using  GMAT Club Forum mobile app

mikemcgarry · Answer

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 :-)

abhimahna · Answer

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.

agar123 · Answer

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

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

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

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