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Which of the figures below can be inscribed in a circle?

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Which of the figures below can be inscribed in a circle? [#permalink] New post 21 Feb 2012, 02:04
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A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

50% (01:40) correct 50% (00:34) wrong based on 117 sessions
Which of the figures below can be inscribed in a circle?

A. 1 only
B. 3 only
C. 1 & 3 only
D. 2 & 3 only
E. 1, 2 & 3
[Reveal] Spoiler: OA

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IMG_0414.jpg [ 2.46 MiB | Viewed 1699 times ]

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Re: PT #2 PS 7 15 [#permalink] New post 21 Feb 2012, 03:10
Expert's post
1
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eybrj2 wrote:
Which of the figures below can be inscribed in a circle?

A. 1 only
B. 3 only
C. 1 & 3 only
D. 2 & 3 only
E. 1, 2 & 3


Useful property: a convex quadrilateral can be inscribed in a circle if and only its opposite angles are supplementary (supplementary angles are two angles that add up to 180°, whereas complementary angles are two angles that add up to 90°). See Central Angle Theorem in Circles chapter of Math Book: math-circles-87957.html.

We can see on the diagram that only I and III meet that requirements.

Answer: C.

Hope it's clear.
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Re: Which of the figures below can be inscribed in a circle? [#permalink] New post 20 Jun 2013, 05:39
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Bumping for review and further discussion*. Get a kudos point for an alternative solution!

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RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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Re: Which of the figures below can be inscribed in a circle? [#permalink] New post 22 Jun 2013, 07:32
eybrj2 wrote:
Which of the figures below can be inscribed in a circle?

A. 1 only
B. 3 only
C. 1 & 3 only
D. 2 & 3 only
E. 1, 2 & 3


Hi Bunnel,
The attachment here cannot be seen.
Can you please re-attach?
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Re: Which of the figures below can be inscribed in a circle? [#permalink] New post 22 Jun 2013, 07:39
Expert's post
cumulonimbus wrote:
eybrj2 wrote:
Which of the figures below can be inscribed in a circle?

A. 1 only
B. 3 only
C. 1 & 3 only
D. 2 & 3 only
E. 1, 2 & 3


Hi Bunnel,
The attachment here cannot be seen.
Can you please re-attach?


I can see it perfectly. Try reloading.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

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; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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: PT #2 PS 7 15 [#permalink] New post 24 Sep 2013, 01:10
Bunuel wrote:
eybrj2 wrote:
Which of the figures below can be inscribed in a circle?

A. 1 only
B. 3 only
C. 1 & 3 only
D. 2 & 3 only
E. 1, 2 & 3


Useful property: a convex quadrilateral can be inscribed in a circle if and only its opposite angles are supplementary (supplementary angles are two angles that add up to 180°, whereas complementary angles are two angles that add up to 90°).

We can see on the diagram that only I and III meet that requirements.

Answer: C.

Hope it's clear.


I agree with "the opposite angles are supplementary" concept and I did the same.
Can this be a solution @Bunuel ?
1. for first diagram - Moreover, isn't the first one isoceles trapezium ? Isn't that sufficient ?
2. for third diagram - Parallelogram inscribed in a circle will become a rectangle (think of shape shifting)
Re: PT #2 PS 7 15   [#permalink] 24 Sep 2013, 01:10
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