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:

We should find the area of triangle with this formula: 0.5*h*b. It is quite easy but we don't know the length of heigh. So what I do in this situation: I just imagine that h equal BC, so the area of triangle is 2*0.5*1=1, but in fact its smaller, because heigh is slightly less than BC. So we can look on answers and define the aproriate value for our triangle area. It is definetly less than 1, sqr(2), sqr(3). So we have two choises: sqr(2)/2 which equals to 1.4/2 or 0.7 and sqr(3)/2 which equals to 1.7/2 or 0.85. I pick the biggest because heigh just SLIGHTLY less then BC. So the answer is B

Re: Geometry Problem Gmat Prep (hard one) [#permalink]

Show Tags

28 Aug 2009, 00:06

4

This post received KUDOS

Quote:

My way

[Obscure] Spoiler: Description We should find the area of triangle with this formula: 0.5*h*b. It is quite easy but we don't know the length of heigh. So what I do in this situation: I just imagine that h equal BC, so the area of triangle is 2*0.5*1=1, but in fact its smaller, because heigh is slightly less than BC. So we can look on answers and define the aproriate value for our triangle area. It is definetly less than 1, sqr(2), sqr(3). So we have two choises: sqr(2)/2 which equals to 1.4/2 or 0.7 and sqr(3)/2 which equals to 1.7/2 or 0.85. I pick the biggest because heigh just SLIGHTLY less then BC. So the answer is B

You should try and avoid assuming any detail in GMAT. Though, you can use a similar way for POE.

Here, the solution is linked to the height of the triangle. Given, BC = 1, Radius = 1. ie OB = OC = 1. Therefore, we can say that /\ OBC is an equilateral triangle. Height of equilateral triangle is SQRT(3)/2 * (side)^2. Therefore, height = SQRT(3)/2. Therefore, area of /\ ABC = (1/2)*2 (Given) * SQRT(3)/2. Area = SQRT(3)/2. Ans : B.

Hope this helps.
_________________

GMAT offended me. Now, its my turn! Will do anything for Kudos! Please feel free to give one.

Re: Geometry Problem Gmat Prep (hard one) [#permalink]

Show Tags

28 Aug 2009, 04:34

bhanushalinikhil wrote:

Quote:

My way

[Obscure] Spoiler: Description We should find the area of triangle with this formula: 0.5*h*b. It is quite easy but we don't know the length of heigh. So what I do in this situation: I just imagine that h equal BC, so the area of triangle is 2*0.5*1=1, but in fact its smaller, because heigh is slightly less than BC. So we can look on answers and define the aproriate value for our triangle area. It is definetly less than 1, sqr(2), sqr(3). So we have two choises: sqr(2)/2 which equals to 1.4/2 or 0.7 and sqr(3)/2 which equals to 1.7/2 or 0.85. I pick the biggest because heigh just SLIGHTLY less then BC. So the answer is B

You should try and avoid assuming any detail in GMAT. Though, you can use a similar way for POE.

Here, the solution is linked to the height of the triangle. Given, BC = 1, Radius = 1. ie OB = OC = 1. Therefore, we can say that /\ OBC is an equilateral triangle. Height of equilateral triangle is SQRT(3)/2 * (side)^2. Therefore, height = SQRT(3)/2. Therefore, area of /\ ABC = (1/2)*2 (Given) * SQRT(3)/2. Area = SQRT(3)/2. Ans : B.

Hope this helps.

Hi Buddy, I like your approach because I did not want to assume it was a rect triangle. But, could you pls explain this : not sure I got it Height of equilateral triangle is SQRT(3)/2 * (side)^2. Therefore, height = SQRT(3)/2. Therefore, area of /\ ABC = (1/2)*2 (Given) * SQRT(3)/2. Area = SQRT(3)/2.

Re: Geometry Problem Gmat Prep (hard one) [#permalink]

Show Tags

28 Aug 2009, 21:00

1

This post received KUDOS

defoue wrote:

bhanushalinikhil wrote:

Quote:

My way

[Obscure] Spoiler: Description We should find the area of triangle with this formula: 0.5*h*b. It is quite easy but we don't know the length of heigh. So what I do in this situation: I just imagine that h equal BC, so the area of triangle is 2*0.5*1=1, but in fact its smaller, because heigh is slightly less than BC. So we can look on answers and define the aproriate value for our triangle area. It is definetly less than 1, sqr(2), sqr(3). So we have two choises: sqr(2)/2 which equals to 1.4/2 or 0.7 and sqr(3)/2 which equals to 1.7/2 or 0.85. I pick the biggest because heigh just SLIGHTLY less then BC. So the answer is B

You should try and avoid assuming any detail in GMAT. Though, you can use a similar way for POE.

Here, the solution is linked to the height of the triangle. Given, BC = 1, Radius = 1. ie OB = OC = 1. Therefore, we can say that /\ OBC is an equilateral triangle. Height of equilateral triangle is SQRT(3)/2 * (side)^2. Therefore, height = SQRT(3)/2. Therefore, area of /\ ABC = (1/2)*2 (Given) * SQRT(3)/2. Area = SQRT(3)/2. Ans : B.

Hope this helps.

Hi Buddy, I like your approach because I did not want to assume it was a rect triangle. But, could you pls explain this : not sure I got it Height of equilateral triangle is SQRT(3)/2 * (side)^2. Therefore, height = SQRT(3)/2. Therefore, area of /\ ABC = (1/2)*2 (Given) * SQRT(3)/2. Area = SQRT(3)/2.

Thx

Sure thing. But what part did you not understand? >Height of equilateral triangle is SQRT(3)/2 * (side)^2 - Its a generic formula. you just have to remember it. >Therefore, height = SQRT(3)/2. >Therefore, area of /\ ABC = (1/2)*2 (Given) * SQRT(3)/2. (Area of triangle formula) >Area = SQRT(3)/2.

I am sorry if I missed something. Please tell me which part would you like to know and I will try my best to help you.
_________________

GMAT offended me. Now, its my turn! Will do anything for Kudos! Please feel free to give one.

Re: Geometry Problem Gmat Prep (hard one) [#permalink]

Show Tags

03 Jul 2010, 13:18

Hi guys, Just one doubt, how can we say that triangle ABC is a right angled triangle given the radius is one & other side BC is one. I mean to say that is there any property for circle that if radius is equal to any one side of the triangle, then the inscribed triangle so formed will be right-angled one?

In the figure above, the radius of circle with center O is 1 and BC = 1. What is the area of triangular region ABC ?

Hi guys, Just one doubt, how can we say that triangle ABC is a right angled triangle given the radius is one & other side BC is one. I mean to say that is there any property for circle that if radius is equal to any one side of the triangle, then the inscribed triangle so formed will be right-angled one?

We know that AC is a diameter. There is a property of a right triangle inscribed in circle:

A right triangle inscribed in a circle must have its hypotenuse as the diameter of the circle. The reverse is also true: if the diameter of the circle is also the triangle’s side, then that triangle is a right triangle and diameter is hypotenuse.

Attachment:

Math_Tri_inscribed.png [ 6.47 KiB | Viewed 39632 times ]

Re: In the figure above, the radius of the circle with center O [#permalink]

Show Tags

24 Apr 2013, 22:12

4

This post received KUDOS

The triangle is a right triangle because one side is the diameter of the circle.

Calculate the third side as \(\sqrt{2^2-1^2}=\sqrt{3}\)

I created a rectangular by translating the triangle (see picture), and the area will be half of the rectangular's. \(AreaRec=b*h=1*\sqrt{3}\) \(AreaTri=\frac{AreaRec}{2}=\sqrt{3}/2\) B

Let me know if this helps

Attachments

sample.JPG [ 16.43 KiB | Viewed 34573 times ]

_________________

It is beyond a doubt that all our knowledge that begins with experience.

Re: In the figure above, the radius of the circle with center O [#permalink]

Show Tags

24 Apr 2013, 22:30

Zarrolou wrote:

The triangle is a right triangle because one side is the diameter of the circle.

Calculate the third side as \(\sqrt{2^2-1^2}=\sqrt{3}\)

I created a rectangular by translating the triangle (see picture), and the area will be half of the rectangular's. \(AreaRec=b*h=1*\sqrt{3}\) \(AreaTri=\frac{AreaRec}{2}=\sqrt{3}/2\) B

Let me know if this helps

You could just use the formula for the area of a triangle which is 1/2xBxH where AB is the height and BC is the base as /_ABC is 90
_________________

When you feel like giving up, remember why you held on for so long in the first place.

We should find the area of triangle with this formula: 0.5*h*b. It is quite easy but we don't know the length of heigh. So what I do in this situation: I just imagine that h equal BC, so the area of triangle is 2*0.5*1=1, but in fact its smaller, because heigh is slightly less than BC. So we can look on answers and define the aproriate value for our triangle area. It is definetly less than 1, sqr(2), sqr(3). So we have two choises: sqr(2)/2 which equals to 1.4/2 or 0.7 and sqr(3)/2 which equals to 1.7/2 or 0.85. I pick the biggest because heigh just SLIGHTLY less then BC. So the answer is B

When a triangle that is right angled as 30, 60 & 90 then the sides opposite to it will be in ratio of 1:\sqrt{3} : 2.

Angle ABC is 90. Triangle OBC is equilateral triangle. Hence, Angle OCB is 60.

In triangle ABC, angle BAC = 180 -90- 60 = 30

Given that AC = 2, BC = 1, hence AB = \sqrt{3}

Therefore area of triangle = 1/2 * 1 * \sqrt{3} = \sqrt{3}/2

Re: In the figure above, the radius of circle with center O is 1 [#permalink]

Show Tags

10 May 2014, 08:57

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

Re: In the figure above, the radius of circle with center O is 1 [#permalink]

Show Tags

15 May 2015, 04:49

The properties that will come in handy here are: (i) In an inscribed triangle, if one side of the triangle is the diagonal of the circle, then that triangle is right angled. So, here, ABC is right angled. (ii) Pythagoras theorem.

So, Area of ABC = (1/2)*BC*AB

From Pythagoras theorem, AB^2 = AC^2 - BC^2 = 2^2 - 1^2 = 3 => AB = root(3)

So, Area of ABC = (1/2)*BC*AB = (1/2)*1*root(3) = root(3)/2

Guyz why the height is not 1. isn't it obvious that the height is also a radius of the circle !!

The height is the perpendicular from a vertex to the opposite side. So, both AB and CB are heights as well as the perpendicular from B to AC. Which one turns to be a radius?
_________________

We should find the area of triangle with this formula: 0.5*h*b. It is quite easy but we don't know the length of heigh. So what I do in this situation: I just imagine that h equal BC, so the area of triangle is 2*0.5*1=1, but in fact its smaller, because heigh is slightly less than BC. So we can look on answers and define the aproriate value for our triangle area. It is definetly less than 1, sqr(2), sqr(3). So we have two choises: sqr(2)/2 which equals to 1.4/2 or 0.7 and sqr(3)/2 which equals to 1.7/2 or 0.85. I pick the biggest because heigh just SLIGHTLY less then BC. So the answer is B

To solve this one you don't even need to use pythagoras formula. It's a right triangle (bcs. Hypotenus=Diameter of the circle) with a hypotenuse of 2 and one side equal to 1. Here you have a 90-60-30 triangle, hence the third side is equal \(\sqrt{3}\) --> \(Area = \sqrt{3}*1/2\) Answer B
_________________

When you’re up, your friends know who you are. When you’re down, you know who your friends are.

Share some Kudos, if my posts help you. Thank you !

Happy New Year everyone! Before I get started on this post, and well, restarted on this blog in general, I wanted to mention something. For the past several months...

It’s quickly approaching two years since I last wrote anything on this blog. A lot has happened since then. When I last posted, I had just gotten back from...

Happy 2017! Here is another update, 7 months later. With this pace I might add only one more post before the end of the GSB! However, I promised that...

The words of John O’Donohue ring in my head every time I reflect on the transformative, euphoric, life-changing, demanding, emotional, and great year that 2016 was! The fourth to...