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# In the diagram below, ABCD is a square with a circle inscribed inside.

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Math Expert
Joined: 02 Sep 2009
Posts: 55274
In the diagram below, ABCD is a square with a circle inscribed inside.  [#permalink]

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17 Jul 2017, 23:36
00:00

Difficulty:

55% (hard)

Question Stats:

61% (01:48) correct 39% (01:53) wrong based on 53 sessions

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In the diagram below, ABCD is a square with a circle inscribed inside. P is a point on the circle. A rectangle AXPY is constructed with A and P as the opposite vertices of the rectangle. What is the length of a side of the square?

(1) AP = 2√2
(2) The line AP coincides with the diagonal AC.

Attachment:

2017-07-18_1034_001.png [ 7.57 KiB | Viewed 746 times ]

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Re: In the diagram below, ABCD is a square with a circle inscribed inside.  [#permalink]

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18 Jul 2017, 02:50
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1
Option 1. is not helpful as point P can be anywhere in the circle
Option 2. For AP to coincide with AC the rectangle AXPY has to be a square. But this too doesnt help us find the lenght of side of the square

Diameter of the circle=side of square=a
Combined, AP=2√2, AC=2√2+a+2√2=a+4√2
Diagonal of a square is a√2, therefore a√2=a+4√2
a=(4√2)/(√2-1)

C IMO

Bunuel wrote:
In the diagram below, ABCD is a square with a circle inscribed inside. P is a point on the circle. A rectangle AXPY is constructed with A and P as the opposite vertices of the rectangle. What is the length of a side of the square?

(1) AP = 2√2
(2) The line AP coincides with the diagonal AC.

Attachment:
2017-07-18_1034_001.png

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Re: In the diagram below, ABCD is a square with a circle inscribed inside.   [#permalink] 18 Jul 2017, 02:50
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