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# A circle C with centre O is inscribed inside rectangle ABCD, such that

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Joined: 22 Aug 2013
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A circle C with centre O is inscribed inside rectangle ABCD, such that  [#permalink]

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22 Jul 2018, 10:55
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35% (medium)

Question Stats:

63% (01:10) correct 38% (01:40) wrong based on 42 sessions

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A circle C with centre O is inscribed inside rectangle ABCD, such that C is the largest possible circle which can be inscribed inside this rectangle, without crossing the sides of rectangle. Is rectangle ABCD a square?

(1) Circle C touches all four sides of rectangle ABCD.

(2) OA = OC.
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Joined: 20 Feb 2015
Posts: 790
Concentration: Strategy, General Management
Re: A circle C with centre O is inscribed inside rectangle ABCD, such that  [#permalink]

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22 Jul 2018, 12:22
amanvermagmat wrote:
A circle C with centre O is inscribed inside rectangle ABCD, such that C is the largest possible circle which can be inscribed inside this rectangle, without crossing the sides of rectangle. Is rectangle ABCD a square?

(1) Circle C touches all four sides of rectangle ABCD.

(2) OA = OC.

Imo -

the largest possible circle , which can be inscribed inside a rectangle will have a diameter equal to the shorter side of the rectangle.

(1) Circle C touches all four sides of rectangle ABCD.
Sufficient !!

(2) OA = OC
does not really guarantee the rectangle to be a square .

A for me !!
Math Expert
Joined: 02 Aug 2009
Posts: 7764
A circle C with centre O is inscribed inside rectangle ABCD, such that  [#permalink]

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22 Jul 2018, 19:15
amanvermagmat wrote:
A circle C with centre O is inscribed inside rectangle ABCD, such that C is the largest possible circle which can be inscribed inside this rectangle, without crossing the sides of rectangle. Is rectangle ABCD a square?

(1) Circle C touches all four sides of rectangle ABCD.

(2) OA = OC.

Hero8888, you have to be careful on the wordings. It is mentioned that it is rectangle

Info given..
1) it is rectangle
2) it has a circle inscribed in it.

Statement I.
Since circle touches all sides, the sides are equal to diameter and both sides are equal.
A rectangle with equal sides is a square.
Sufficient

Statement II.
OA=OC
nothing much
Insufficient

A
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Re: A circle C with centre O is inscribed inside rectangle ABCD, such that  [#permalink]

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22 Jul 2018, 19:19
chetan2u wrote:
amanvermagmat wrote:
A circle C with centre O is inscribed inside rectangle ABCD, such that C is the largest possible circle which can be inscribed inside this rectangle, without crossing the sides of rectangle. Is rectangle ABCD a square?

(1) Circle C touches all four sides of rectangle ABCD.

(2) OA = OC.

Hero8888, you have to be careful on the wordings. It is mentioned that it is rectangle

Info given..
1) it is rectangle
2) it has a circle inscribed in it.

Statement I.
Since circle touches all sides, the sides are equal to diameter and both sides are equal.
A rectangle with equal sides is a square.
Sufficient

Statement II.
OA=OC
nothing much
Insufficient

A

My bad. Deleting my previous post.
Re: A circle C with centre O is inscribed inside rectangle ABCD, such that   [#permalink] 22 Jul 2018, 19:19
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