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Is the Triangle ABC right angled at C?

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Is the Triangle ABC right angled at C?  [#permalink]

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New post 23 Jun 2015, 02:08
3
00:00
A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

70% (00:47) correct 30% (01:02) wrong based on 130 sessions

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Is the Triangle ABC right angled at C?

1) AB is not the longest chord that can be drawn in a circle.

2) The Length of AB is seven-fifth the radius of the circle.
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Re: Is the Triangle ABC right angled at C?  [#permalink]

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New post 23 Jun 2015, 02:51
monk16 wrote:
Is the Triangle ABC right angled at C?

1) AB is not the longest chord that can be drawn in a circle.

2) The Length of AB is seven-fifth the radius of the circle.


A right triangle's hypotenuse is a diameter of its circumcircle (circumscribed circle).
The reverse is also true: if one of the sides of an inscribed triangle is a diameter of the circle, then the triangle is a right angled
(right angel being the angle opposite the diameter/hypotenuse).
Image

Is the Triangle ABC right angled at C?

According to the above if ABC is right angled at C, then AB (hypotenuse) must be the diameter of circumscribed circle.

(1) AB is not the longest chord that can be drawn in a circle. Diameter is the longest chord possible in a circle, thus AB is NOT a diameter, therefore ABC is not right angled at C. Sufficient.

(2) The Length of AB is seven-fifth the radius of the circle. If ABC were right angled at C, AB would be a diameter, thus equal to twice the radius of the circle. ABC is not right angled at C. Sufficient.

Answer: D.

Attachment:
2015-06-23_1445.png
2015-06-23_1445.png [ 13.04 KiB | Viewed 1792 times ]

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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. ,11 Mixed Questions, 12 Fresh Meat

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., 11 New DS set.


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Re: Is the Triangle ABC right angled at C?  [#permalink]

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New post 23 Jun 2015, 02:59
1
Bunuel wrote:
monk16 wrote:
Is the Triangle ABC right angled at C?

1) AB is not the longest chord that can be drawn in a circle.

2) The Length of AB is seven-fifth the radius of the circle.


A right triangle's hypotenuse is a diameter of its circumcircle (circumscribed circle).
The reverse is also true: if one of the sides of an inscribed triangle is a diameter of the circle, then the triangle is a right angled
(right angel being the angle opposite the diameter/hypotenuse).
Image

Is the Triangle ABC right angled at C?

According to the above if ABC is right angled at C, then AB (hypotenuse) must be the diameter of circumscribed circle.

(1) AB is not the longest chord that can be drawn in a circle. Diameter is the longest chord possible in a circle, thus AB is NOT a diameter, therefore ABC is not right angled at C. Sufficient.

(2) The Length of AB is seven-fifth the radius of the circle. If ABC were right angled at C, AB would be a diameter, thus equal to twice the radius of the circle. ABC is not right angled at C. Sufficient.

Answer: D.

Attachment:
2015-06-23_1445.png


How do we know that C lies on circle and not in circle or out of circle?
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Re: Is the Triangle ABC right angled at C?  [#permalink]

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New post 23 Jun 2015, 03:02
Harley1980 wrote:
Bunuel wrote:
monk16 wrote:
Is the Triangle ABC right angled at C?

1) AB is not the longest chord that can be drawn in a circle.

2) The Length of AB is seven-fifth the radius of the circle.


A right triangle's hypotenuse is a diameter of its circumcircle (circumscribed circle).
The reverse is also true: if one of the sides of an inscribed triangle is a diameter of the circle, then the triangle is a right angled
(right angel being the angle opposite the diameter/hypotenuse).
Image

Is the Triangle ABC right angled at C?

According to the above if ABC is right angled at C, then AB (hypotenuse) must be the diameter of circumscribed circle.

(1) AB is not the longest chord that can be drawn in a circle. Diameter is the longest chord possible in a circle, thus AB is NOT a diameter, therefore ABC is not right angled at C. Sufficient.

(2) The Length of AB is seven-fifth the radius of the circle. If ABC were right angled at C, AB would be a diameter, thus equal to twice the radius of the circle. ABC is not right angled at C. Sufficient.

Answer: D.

Attachment:
2015-06-23_1445.png


How do we know that C lies on circle and not in circle or out of circle?


Original question (I've seen it somewhere) has an image showing that ABC is inscribed in a circle.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

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. ,11 Mixed Questions, 12 Fresh Meat

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., 11 New DS set.


What are GMAT Club Tests?
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Math Expert
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Joined: 02 Sep 2009
Posts: 51227
Re: Is the Triangle ABC right angled at C?  [#permalink]

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New post 23 Jun 2015, 03:32
1
Harley1980 wrote:
Bunuel wrote:
monk16 wrote:
Is the Triangle ABC right angled at C?

1) AB is not the longest chord that can be drawn in a circle.

2) The Length of AB is seven-fifth the radius of the circle.


A right triangle's hypotenuse is a diameter of its circumcircle (circumscribed circle).
The reverse is also true: if one of the sides of an inscribed triangle is a diameter of the circle, then the triangle is a right angled
(right angel being the angle opposite the diameter/hypotenuse).
Image

Is the Triangle ABC right angled at C?

According to the above if ABC is right angled at C, then AB (hypotenuse) must be the diameter of circumscribed circle.

(1) AB is not the longest chord that can be drawn in a circle. Diameter is the longest chord possible in a circle, thus AB is NOT a diameter, therefore ABC is not right angled at C. Sufficient.

(2) The Length of AB is seven-fifth the radius of the circle. If ABC were right angled at C, AB would be a diameter, thus equal to twice the radius of the circle. ABC is not right angled at C. Sufficient.

Answer: D.

Attachment:
2015-06-23_1445.png


How do we know that C lies on circle and not in circle or out of circle?


Thank you for an idea of a question. :-D
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

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. ,11 Mixed Questions, 12 Fresh Meat

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., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Retired Moderator
User avatar
Joined: 06 Jul 2014
Posts: 1235
Location: Ukraine
Concentration: Entrepreneurship, Technology
GMAT 1: 660 Q48 V33
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Re: Is the Triangle ABC right angled at C?  [#permalink]

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New post 23 Jun 2015, 05:22
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Re: Is the Triangle ABC right angled at C?  [#permalink]

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Re: Is the Triangle ABC right angled at C? &nbs [#permalink] 28 Feb 2018, 15:11
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