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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]

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New post 21 Feb 2012, 03:04
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Which of the figures below can be inscribed in a circle?
Image
(A) I only
(B) III only
(C) I & III only
(D) II & III only
(E) I, II & III

[Reveal] Spoiler:
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Re: Which of the figures below can be inscribed in a circle? [#permalink]

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New post 21 Feb 2012, 04:10
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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]

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New post 20 Jun 2013, 06:39
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Re: Which of the figures below can be inscribed in a circle? [#permalink]

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New post 22 Jun 2013, 08:32
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]

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New post 22 Jun 2013, 08:39
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Re: Which of the figures below can be inscribed in a circle? [#permalink]

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New post 24 Sep 2013, 02:10
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)
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Re: Which of the figures below can be inscribed in a circle? [#permalink]

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Re: Which of the figures below can be inscribed in a circle? [#permalink]

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New post 20 Jun 2015, 03:26
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°). 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.


Hi Bunuel,
By 'opposite angles' you mean diagonally opposite angles right? otherwise even II can be inscribed in a circle.
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Re: Which of the figures below can be inscribed in a circle? [#permalink]

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New post 20 Jun 2015, 03:39
Expert's post
NavenRk wrote:
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°). 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.


Hi Bunuel,
By 'opposite angles' you mean diagonally opposite angles right? otherwise even II can be inscribed in a circle.


Yes Diagonally opposite angles should sum up to 180 degree for the quadrilateral to be inscribed in a circle.

This property is a derived property from the one which says that angle subtended by any segment at the centre of the circle should be twice the angle subtended by the same segment on the circumference of the same circle.

Such Quadrilaterals which can be inscribed in a circle are called "Cyclic Quadrilateral"
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Re: Which of the figures below can be inscribed in a circle?   [#permalink] 20 Jun 2015, 03:39
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