Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

Re: What is b in the circle shown above? [#permalink]

Show Tags

12 Mar 2017, 20:36

vmelgargalan wrote:

hey, I am confused as to c=a in this case. could you explain this?

The STE 1 can be made from the figure using the theory of similar triangles. using Pythagorean theory we can make an equation with only one variable. B is sufficient
_________________

1) b is a common side to both the right angled triangles 2) Both the triangles have one common angle (90 degrees)

So, c/a = b/b => c=a

And by using Pythagoras theorem, 84= (b*b) + (5 * 5)

Hence Statement 2 alone is sufficient.

Kudos +1 guys!

per your logic, each triangle inscribed in a circle is a isosceles right triangle. I think you are confusing it with another property or similar triangles i.e ratio of area = square of the ratio of sides

Re: What is b in the circle shown above? [#permalink]

Show Tags

12 Jul 2017, 13:59

JanarthCj wrote:

From the given data,

1) b is a common side to both the right angled triangles 2) Both the triangles have one common angle (90 degrees)

So, c/a = b/b => c=a

And by using Pythagoras theorem, 84= (b*b) + (5 * 5)

Hence Statement 2 alone is sufficient.

Kudos +1 guys!

Could you please explain how do you know that the triangles are similar? Based on the given information, don't you need to confirm that an additional pair of sides is similar, or that an additional pair of angles is equal?

From the information and attached figure we can derive:

angle PQR = angle QOR = 90 degrees ---(1) angle PRQ = angle QRO = x degrees ----(2) From 1 and 2 and AAA similarity ===> angle QPR = angle QQR = y degrees

Therefore the triangles PQR and QOR are similar PQ/QR = QO/OR ==> a/c = b/5 ==>bc =5a.........(3)

Statement 1 ==> Same as can be derived from given information and insufficient since various combinations exist Statement 1 ==> From (3), a = √84 and b^2 + 5^2 = C^2 (since QOR is a right angle triangle) we can get the value of b

From the information and attached figure we can derive:

angle PQR = angle QOR = 90 degrees ---(1) angle PRQ = angle QRO = x degrees ----(2) From 1 and 2 and AAA similarity ===> angle QPR = angle QQR = y degrees

Therefore the triangles PQR and QOR are similar PQ/QR = QO/OR ==> a/c = b/5 ==>bc =5a.........(3)

Statement 1 ==> Same as can be derived from given information and insufficient since various combinations exist Statement 1 ==> From (3), a = √84 and b^2 + 5^2 = C^2 (since QOR is a right angle triangle) we can get the value of b

Re: What is b in the circle shown above? [#permalink]

Show Tags

06 Sep 2017, 08:39

with a value as rt(84), we can find the value of diameter in terms of x+5 for triangle PQR and using the A value we can find length of x in terms of b and so on create a equation and by solving it we will get b x as 7 and b as rt(35).

I got it wrong but I'll provide my approach after thinking about it, to see if I can help.

Problem: DS to find b The information provided by the problem is: 1. Two triangles with a common side and adjacent angles of 90º angle (lets name it L). 2. Triangle QRL measures: 5-b-c, angles Q,R,90º. Looks like 30-60-90 but there is no certainty, still pitagoras can be applied. 3. One big triangle PQR that is isoceles Right triangle (because internal angles theory, the diameter shows that the angle is 90º). And is inside a circle so pitagoras is possible. Mental note: Get a side then can apply "30-60-90, x- x√3, 2x" or Pitagoras.

Statements: (1) bc=5a Can't apply pitagoras or "30,60,90" Not Sufficient -> BCE

2) PQ = √84 One side! So can apply pitagoras and "30-60-90" Can find C! with C then can find b with pitagoras. Sufficient -> B

I got it wrong but I'll provide my approach after thinking about it, to see if I can help.

Problem: DS to find b The information provided by the problem is: 1. Two triangles with a common side and adjacent angles of 90º angle (lets name it L). 2. Triangle QRL measures: 5-b-c, angles Q,R,90º. Looks like 30-60-90 but there is no certainty, still pitagoras can be applied. 3. One big triangle PQR that is isoceles Right triangle (because internal angles theory, the diameter shows that the angle is 90º). And is inside a circle so pitagoras is possible. Mental note: Get a side then can apply "30-60-90, x- x√3, 2x" or Pitagoras.

Statements: (1) bc=5a Can't apply pitagoras or "30,60,90" Not Sufficient -> BCE

2) PQ = √84 One side! So can apply pitagoras and "30-60-90" Can find C! with C then can find b with pitagoras. Sufficient -> B

Your entire solution is based that it's 30-60-90, triangle, which we don't know

Re: What is b in the circle shown above? [#permalink]

Show Tags

17 Nov 2017, 05:50

cbh wrote:

PaterD wrote:

I got it wrong but I'll provide my approach after thinking about it, to see if I can help.

Problem: DS to find b The information provided by the problem is: 1. Two triangles with a common side and adjacent angles of 90º angle (lets name it L). 2. Triangle QRL measures: 5-b-c, angles Q,R,90º. Looks like 30-60-90 but there is no certainty, still pitagoras can be applied. 3. One big triangle PQR that is isoceles Right triangle (because internal angles theory, the diameter shows that the angle is 90º). And is inside a circle so pitagoras is possible. Mental note: Get a side then can apply "30-60-90, x- x√3, 2x" or Pitagoras.

Statements: (1) bc=5a Can't apply pitagoras or "30,60,90" Not Sufficient -> BCE

2) PQ = √84 One side! So can apply pitagoras and "30-60-90" Can find C! with C then can find b with pitagoras. Sufficient -> B

Your entire solution is based that it's 30-60-90, triangle, which we don't know

I thought that kind o trick was more known or used... Is a shortcut that can be used on right triangle that has the following angle measures has: Angle measures: 90- 60 - 30 Side measures: 2x - x√3 - x

Is similar for equilateral: Angle measures: 90- 45 - 45 Side measures: x√2 - x - x

Still the more possible approaches the better, this one is a hard one

I thought that kind o trick was more known or used... Is a shortcut that can be used on right triangle that has the following angle measures has: Angle measures: 90- 60 - 30 Side measures: 2x - x√3 - x

Is similar for equilateral: Angle measures: 90- 45 - 45 Side measures: x√2 - x - x

Still the more possible approaches the better, this one is a hard one

You just know that this is right triangle. That's it Actually there are 3 right triangles, which are similar to each other, so basically that kind of question could be solved through similarity but I don't see how that can be solved via option B only

Bunuel wrote:

can you please elaborate it? I'm confused a bit, much appreciated!

Re: What is b in the circle shown above? [#permalink]

Show Tags

17 Nov 2017, 08:23

cbh wrote:

PaterD wrote:

I thought that kind o trick was more known or used... Is a shortcut that can be used on right triangle that has the following angle measures has: Angle measures: 90- 60 - 30 Side measures: 2x - x√3 - x

Is similar for equilateral: Angle measures: 90- 45 - 45 Side measures: x√2 - x - x

Still the more possible approaches the better, this one is a hard one

You just know that this is right triangle. That's it Actually there are 3 right triangles, which are similar to each other, so basically that kind of question could be solved through similarity but I don't see how that can be solved via option B only

Bunuel wrote:

can you please elaborate it? I'm confused a bit, much appreciated!

Dude you are right.... I assumed the angle measures

I'll call some cavalry to solve this as I can't see a proper way to crack this nut VeritasPrepKarishma could you please help us with this?