|
Author |
Message |
|
VP
Joined: 30 Jun 2008
Posts: 1050
Followers: 8
Kudos [?]:
214
[0], given: 1
|
M20 #07 : TRIANGLE INSIDE A CIRCLE [#permalink]
 12 Oct 2008, 10:53
Question Stats:
57% (01:37) correct
42% (00:53) wrong based on 87 sessions
Points A, B, and C lie on a circle of radius 1. What is the area of triangle ABC ? 1. AB^2 = BC^2 + AC^2 2. \angle CAB equals 30 degrees Source: GMAT Club Tests - hardest GMAT questions
_________________
"You have to find it. No one else can find it for you." - Bjorn Borg
Check out my GMAT blog - GMAT Tips and Strategies
|
|
|
|
|
|
|
|
|
GMAT Club team member
Joined: 02 Sep 2009
Posts: 11610
Followers: 1800
Kudos [?]:
9593
[3] , given: 828
|
Re: M20 #07 : TRIANGLE INSIDE A CIRCLE [#permalink]
01 Feb 2011, 15:19
3
This post received
KUDOS
adinit wrote: S2 says angle CAB is 30 degree. Can't we find other angles of the triangle and apply 1:\sqrt{3}:2 equatio to find sides. The sides of a triangle are always in the ratio 1:\sqrt{3}:2 when we have 30°-60°-90° right triangle but knowing that just one angle of the inscribed triangle equals to 30° does not mean that we have this case. Points A, B, and C lie on a circle of radius 1. What is the area of triangle ABC?(1) AB^2 = BC^2 + AC^2 --> triangle ABC is a right triangle with AB as hypotenuse --> area=\frac{BC*AC}{2}. Now, 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 hypotenuse, then that triangle is a right triangle). So, hypotenuse AB=diameter=2*radius=2, but just knowing the length of the hypotenuse is not enough to calculate the legs of a right triangle thus we can not get the area. Not sufficient. (2) \angle CAB equals 30 degrees. Clearly insufficient. (1)+(2) From (1) ABC is a right triangle and from (2) \angle CAB=30 --> we have 30°-60°-90° right triangle and as AB=hypotenuse=2 then the legs equal to 1 and \sqrt{3} --> area=\frac{BC*AC}{2}=\frac{\sqrt{3}}{2}. Sufficient. Answer: C.
_________________
PLEASE READ AND FOLLOW: 11 Rules for Posting!!!
RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory
COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. NEW!!!
DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set. NEW!!!
What are GMAT Club Tests?
25 extra-hard Quant Tests
Find out what's new at GMAT Club - latest features and updates
|
|
|
|
|
|
Senior Manager
Status: ready to boMBArd
Joined: 31 Oct 2010
Posts: 493
Location: India
Concentration: Entrepreneurship, Strategy
GMAT 1: 710 Q48 V40
WE: Project Management (Manufacturing)
Followers: 10
Kudos [?]:
31
[1] , given: 67
|
Re: M20 #07 : TRIANGLE INSIDE A CIRCLE [#permalink]
03 Feb 2011, 07:00
1
This post received
KUDOS
amitdgr wrote: Points A, B, and C lie on a circle of radius 1. What is the area of triangle ABC ? 1. AB^2 = BC^2 + AC^2 2. \angle CAB equals 30 degrees Source: GMAT Club Tests - hardest GMAT questions Statement 1: Tells us ABC is a right triangle. Property of a right triangle inscribed within a circle- The hypotenuse of the triangle is necessarily the diameter of the circle the triangle is inscribed within. So we know the hypotenuse=2. However, 2 find the area, we need to know the other 2 sides as well and with this statement alone, we have no means to find those. So, this statement alone is insufficient. Statement 2: Tells us one angle is 30 degrees. This information alone cannot lead us to find anything at all. (1) and (2) combined: Tells us that the triangle is a 30-60-90 one. From (1), we know that the biggest side is 2. In a 30-60-90 triangle, the sides are in the ratio of 1:\sqrt{3}:2, where 1 represents smallest side. So, the legs of the triangle will be 1 and \sqrt{3} and thats all the information we need to find out the area. You can go ahead and solve the problem but since its a DS question, that is unnecessary. Answer: C
_________________
My GMAT debrief: from-620-to-710-my-gmat-journey-114437.html
|
|
|
|
|
|
Manager
Joined: 09 Oct 2008
Posts: 95
Followers: 1
Kudos [?]:
4
[0], given: 0
|
Re: m20#7 : TRIANGLE INSIDE A CIRCLE [#permalink]
12 Oct 2008, 11:06
IMO A:
A says triangle is right angle triangle..now and A and B lies on diameter and C on cirle..
OC will be 1 so we can get area of triangle..there is some equation which can calculate area when we have Hypo.lengh and altitude (OC)
B is not suff. we do not know is base on diameter or not.
Thanks
|
|
|
|
|
|
VP
Joined: 17 Jun 2008
Posts: 1411
Followers: 6
Kudos [?]:
73
[0], given: 0
|
Re: m20#7 : TRIANGLE INSIDE A CIRCLE [#permalink]
12 Oct 2008, 11:09
amitdgr wrote: Points A, B, and C lie on a circle of radius 1. What is the area of triangle ABC ?
1. AB^2 = BC^2 + AC^2
2. \angle CAB equals 30 degrees
(C) 2008 GMAT Club - m20#7 1) does not provide clue on whats the height of triangle BC and AC can be at any angle !!hence we cannot get the height 2)does not provide info about angles combine both we can get the area ABsin@ can be used
_________________
cheers
Its Now Or Never
|
|
|
|
|
|
Manager
Joined: 16 Apr 2008
Posts: 96
Followers: 1
Kudos [?]:
15
[0], given: 7
|
Re: M20 #07 : TRIANGLE INSIDE A CIRCLE [#permalink]
30 Apr 2010, 05:30
IMO C
A. No clue on height. Only says it is a Right Angled Triangle with <B =90.
B. No clue on other sides or angles. <C=30
Combining, AB=2 (diameter) and we can use AB sinC.
-Prabir
|
|
|
|
|
|
Intern
Joined: 09 Nov 2009
Posts: 11
Followers: 0
Kudos [?]:
2
[0], given: 0
|
Re: M20 #07 : TRIANGLE INSIDE A CIRCLE [#permalink]
30 Apr 2010, 07:55
S = (BC∙AC)/2
BC = 1/2∙AB,
=>
AB² = BC² + AC² => AB² = 1/4∙AB² + AC²
AC = (√3)/2∙AB
=>
S = ((1/2∙AB)∙(√3/2∙AB))/2
S = (√3/8)AB²
|
|
|
|
|
|
Manager
Joined: 18 Mar 2010
Posts: 90
Location: United States
GMAT 1: Q V
Followers: 2
Kudos [?]:
22
[0], given: 5
|
Re: M20 #07 : TRIANGLE INSIDE A CIRCLE [#permalink]
30 Apr 2010, 13:10
ykpgal wrote: S = (BC∙AC)/2
BC = 1/2∙AB,
=>
AB² = BC² + AC² => AB² = 1/4∙AB² + AC²
AC = (√3)/2∙AB
=>
S = ((1/2∙AB)∙(√3/2∙AB))/2
S = (√3/8)AB² Um, no idea what you did here. I see S = the area, but it looks like you didn't find a value for the area. I also don't see how some people have mentioned that the base of the triangle lies along the diameter. All we know is that the triangle is inscribed inside the circle. I got C. I don't know how to find the area, but I know it's possible. St 1 tells us it's a right triangle, since the square of one side, equals the sum of the squares of the other two sides. But as there could be many different sizes of right traingles that would fit insiade this circle, this statement is insufficient. St2 gives us another one of the angles. Like statement one, alone it is insufficent, but together we know know this is a 30-60-90 triangle. This will fit into this circle only one way. I don't care that I can't figure out the area, only that I know it's possible.
|
|
|
|
|
|
Director
Joined: 21 Dec 2009
Posts: 592
Concentration: Entrepreneurship, Finance
Followers: 13
Kudos [?]:
130
[0], given: 20
|
Re: M20 #07 : TRIANGLE INSIDE A CIRCLE [#permalink]
30 Apr 2010, 15:18
(1) implies a Pythagorean triple of diameter (a side) 2 units. Height and other angles are unknown, so Insufficient. (2) we can't find area of a triangle with just an angle given. Insufficient (1) and (2): implies a triangle with 30(1) : 60(sqr{3} : 90(2) angle - sides combination. So, Sufficient.
_________________
KUDOS me if you feel my contribution has helped you.
Last edited by gmatbull on 01 May 2010, 17:48, edited 1 time in total.
|
|
|
|
|
|
Manager
Joined: 04 Dec 2009
Posts: 76
Location: INDIA
Followers: 2
Kudos [?]:
6
[0], given: 4
|
Re: M20 #07 : TRIANGLE INSIDE A CIRCLE [#permalink]
30 Apr 2010, 20:49
OA is C from S1- we only know triangle is right angle. from S2-we only know one angle is 30 deg. from 1+2 we can find the area.
_________________
MBA (Mind , Body and Attitude )
|
|
|
|
|
|
Manager
Joined: 18 Mar 2010
Posts: 90
Location: United States
GMAT 1: Q V
Followers: 2
Kudos [?]:
22
[0], given: 5
|
Re: M20 #07 : TRIANGLE INSIDE A CIRCLE [#permalink]
04 May 2010, 13:59
nifoui wrote: gmatbull wrote: (1) implies a Pythagorean triple of diameter (a side) 2 units.
Height and other angles are unknown, so Insufficient.
(2) we can't find area of a triangle with just an angle given.
Insufficient
(1) and (2): implies a triangle with 30(1) : 60(sqr{3} : 90(2)
angle - sides combination. So, Sufficient. How do we know that statement 1 implies a pythagorean theorem? I don't understand the formula in statement 1... Help? The formula in statement 1 says the length of side AB squared equals the the sum of the squares of the other two sides (BC and AC). This is the pythagorean theorem. When I first looked at the equation, I was thinking A*B^2 but then I realized what kind of equation I was looking at and knew AB was the length of the side from A to B. Seems like others saw the same thing at first.
|
|
|
|
|
|
Senior Manager
Joined: 21 Dec 2009
Posts: 268
Location: India
Followers: 5
Kudos [?]:
41
[0], given: 25
|
Re: M20 #07 : TRIANGLE INSIDE A CIRCLE [#permalink]
20 May 2010, 08:54
amitdgr wrote: Points A, B, and C lie on a circle of radius 1. What is the area of triangle ABC ? 1. AB^2 = BC^2 + AC^2 2. \angle CAB equals 30 degrees Source: GMAT Club Tests - hardest GMAT questions Area of triangle = (1/2)*height * base Now stmt 1: AB^2 = BC^2 + AC^2 from here AB is the hypotenuse of the triangle and \angle BCA is 90 degree So, AB is the diameter which is 2 unit So we know the base of the triangle but we do not know the height of the trianle stmt 2: we have \angle CAB[/m] equals 30 degrees This will help us find the height of the triangle using sine and cos formulae Voilà we got both base and height. So, answer is C.
_________________
Cheers,
SD
|
|
|
|
|
|
Intern
Joined: 02 Nov 2010
Posts: 47
Followers: 0
Kudos [?]:
0
[0], given: 23
|
Re: M20 #07 : TRIANGLE INSIDE A CIRCLE [#permalink]
04 May 2011, 15:21
I got C.
1. statement tells that it is a right triangle and AB is hypotenuse . Meaning the length is 2 (2xradius)
2 I took the statement to mean that it was a 30,60,90 triangle.
Is my reasoning correct?
|
|
|
|
|
|
VP
Status: There is always something new !!
Affiliations: PMI,QAI Global,eXampleCG
Joined: 08 May 2009
Posts: 1400
Followers: 8
Kudos [?]:
84
[0], given: 10
|
Re: M20 #07 : TRIANGLE INSIDE A CIRCLE [#permalink]
04 May 2011, 23:35
a essentially its a triangle in semi circle.Altitude measurement is not given. b not sufficient. a+b gives 3^1/2 and 1 as the measurements. Hence C.
_________________
Visit -- http://www.sustainable-sphere.com/
Promote Green Business,Sustainable Living and Green Earth !!
|
|
|
|
|
|
Manager
Joined: 15 Apr 2011
Posts: 65
Location: Bangalore India
Schools: LBS, HBS, ISB, Kelloggs, INSEAD
Followers: 2
Kudos [?]:
3
[0], given: 2
|
Re: M20 #07 : TRIANGLE INSIDE A CIRCLE [#permalink]
05 May 2011, 04:23
amitdgr wrote: Points A, B, and C lie on a circle of radius 1. What is the area of triangle ABC ? 1. AB^2 = BC^2 + AC^2 2. \angle CAB equals 30 degrees Source: GMAT Club Tests - hardest GMAT questions I dont think that statement A is sufficient. As C can be anywhere on the circle. So we do not get the hight every time we connect O to C which means the area of the triangle can not be determined by 1 alone. St 2 is also not sufficient. But if we combine 1 and 2, we get all the angles of triangle which are 30, 60 and 90 degrees. and the length of the hypotenuse by which we can calculate other sides as well. AB = 2 AC = sqrt(3) and BC = 1. so the area = (1/2)*Base*Height = (1/2)*1*sqrt(3) = sqrt(3)/2 so my answer is together the statements are sufficient.
_________________
Thanks,
AM
|
|
|
|
|
|
Senior Manager
Status: ready to boMBArd
Joined: 31 Oct 2010
Posts: 493
Location: India
Concentration: Entrepreneurship, Strategy
GMAT 1: 710 Q48 V40
WE: Project Management (Manufacturing)
Followers: 10
Kudos [?]:
31
[0], given: 67
|
Re: M20 #07 : TRIANGLE INSIDE A CIRCLE [#permalink]
05 May 2011, 07:53
havok wrote: Is statement one an equation that people memorized? I don't see the 90 degree angle reference. Thats Pythagoras Theorem for you. It States that In a 90 degree triangle, the square of the longest side is equal to the sum of the squares of the other two sides. This is an exclusive property of 90 degree triangles. So, if you happen to see a triangle with sides AB, BC and AC and if it is mentioned that AB^2= BC^2+AC^2, you can be sure that its a 90 degree triangle and that AB is the longest side (the hypotenuse) Problems based on Pythagoras theorem are extremely common on the GMAT. Follow this link for more: math-triangles-87197.html There is a topic on Right Triangle in this chapter.
_________________
My GMAT debrief: from-620-to-710-my-gmat-journey-114437.html
|
|
|
|
|
|
Intern
Joined: 17 Dec 2010
Posts: 13
Followers: 0
Kudos [?]:
0
[0], given: 0
|
Re: M20 #07 : TRIANGLE INSIDE A CIRCLE [#permalink]
05 May 2011, 11:16
stmt 1: from here AB is the hypotenuse of the triangle and \angle BCA is 90 degree
So, AB is the diameter which is 2 unit
So we know the base of the triangle but we do not know the height of the trianle
stmt 2: we have \angle CAB[/m] equals 30 degrees
This will help us find the height of the triangle using sine and cos formulae
Voilà we got both base and height. So, answer is C
|
|
|
|
|
|
Senior Manager
Joined: 11 May 2011
Posts: 383
Location: US
Followers: 1
Kudos [?]:
46
[0], given: 46
|
Re: M20 #07 : TRIANGLE INSIDE A CIRCLE [#permalink]
11 May 2011, 20:46
Hi Folks, This is my first post and i would like to take this opportunity to answer this question. Answer is C. Reason - a) AB is diameter = 2. Angle ACB = 90. but ration od AC &AB not clear. Insufficient. b) Angle CAB is 30 degree. Insufficient. a) +b) value of AC and AB can be calculated because CAB is 30 degree. and since it is right angle triangle - Area will be (AC+CB)/2. Answer C. Cheers, Aj.
_________________
-----------------------------------------------------------------------------------------
What you do TODAY is important because you're exchanging a day of your life for it!
-----------------------------------------------------------------------------------------
|
|
|
|
|
|
Manager
Joined: 13 May 2010
Posts: 125
Followers: 0
Kudos [?]:
2
[0], given: 4
|
Re: M20 #07 : TRIANGLE INSIDE A CIRCLE [#permalink]
22 Feb 2012, 15:03
Why does statement 1 necessary convey the idea of a right triangle.....In one of the gmat club test questions I saw a property -
For triangles which has all acute angles there are, two cases where this property is true
such as AB^2 = BC^2 + AC^2 and BC^2 = AB^2 + AB^2
For triangle with an obtuse angle, AB^2 < BC^2 + AC ^2
For right angled triangle, there is only one case of AB ^2 = BC^2 + AC^2 (as opposed to two cases as found in acute angled triangle)
Then why will statement A necessarily suggest a right angled triangle, it can also be an a triangle with all acute angles.
|
|
|
|
|
|
GMAT Club team member
Joined: 02 Sep 2009
Posts: 11610
Followers: 1800
Kudos [?]:
9593
[0], given: 828
|
Re: M20 #07 : TRIANGLE INSIDE A CIRCLE [#permalink]
22 Feb 2012, 15:27
teal wrote: Why does statement 1 necessary convey the idea of a right triangle.....In one of the gmat club test questions I saw a property -
For triangles which has all acute angles there are, two cases where this property is true
such as AB^2 = BC^2 + AC^2 and BC^2 = AB^2 + AB^2
For triangle with an obtuse angle, AB^2 < BC^2 + AC ^2
For right angled triangle, there is only one case of AB ^2 = BC^2 + AC^2 (as opposed to two cases as found in acute angled triangle)
Then why will statement A necessarily suggest a right angled triangle, it can also be an a triangle with all acute angles. Where did you see that? It's not true. Must know for the GMAT: converse of the Pythagorean theorem is also true.For any triangle with sides a, b, c, if a^2 + b^2 = c^2, then the angle between a and b measures 90°. Generally if c is the longest of the three sides of a triangle then:If a^2 + b^2 = c^2, then the triangle is right. If a^2 + b^2 > c^2, then the triangle is acute. If a^2 + b^2 < c^2, then the triangle is obtuse. Hope it helps.
_________________
PLEASE READ AND FOLLOW: 11 Rules for Posting!!!
RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory
COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. NEW!!!
DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set. NEW!!!
What are GMAT Club Tests?
25 extra-hard Quant Tests
Find out what's new at GMAT Club - latest features and updates
|
|
|
|
|
|
|
Re: M20 #07 : TRIANGLE INSIDE A CIRCLE
[#permalink]
22 Feb 2012, 15:27
|
|
|
|
|
|
|
|
|
|
|
close
