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# What is the perimeter of quadrangle ABCD in which a circle is inscribe

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Math Expert
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What is the perimeter of quadrangle ABCD in which a circle is inscribe  [#permalink]

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29 Jul 2016, 04:00
1
15
00:00

Difficulty:

85% (hard)

Question Stats:

34% (01:24) correct 66% (01:48) wrong based on 150 sessions

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What is the perimeter of quadrangle ABCD in which a circle is inscribed?

(1) AB + DC = 8
(2) BC = 5

Attachment:

untitled.JPG [ 5.22 KiB | Viewed 2303 times ]

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Re: What is the perimeter of quadrangle ABCD in which a circle is inscribe  [#permalink]

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03 Nov 2016, 22:39
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Bunuel wrote:

What is the perimeter of quadrangle ABCD in which a circle is inscribed?

(1) AB + DC = 8
(2) BC = 5

Attachment:
The attachment untitled.JPG is no longer available

Please check the detailed explanation in the attached picture

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##### General Discussion
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Re: What is the perimeter of quadrangle ABCD in which a circle is inscribe  [#permalink]

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29 Jul 2016, 09:29
1
2
there can be only two tangents to a circle from any exterior pt. and they are of equal length.. (i.e. from pt. of origin to pt. of contact...
SO the perimeter of the quadilateral will be effectively 2 ( AB + DC )...

so il go with A..
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Re: What is the perimeter of quadrangle ABCD in which a circle is inscribe  [#permalink]

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02 Nov 2016, 15:53
Can someone please explain this? I don't understand the underlying concept.

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Re: What is the perimeter of quadrangle ABCD in which a circle is inscribe  [#permalink]

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03 Nov 2016, 07:54
lawiniecke wrote:
Can someone please explain this? I don't understand the underlying concept.

Refer the attached figure.

Draw a line from center O to corner C. Now, consider triangles ROC and QOC. Since OR = OQ and hypotenuse OC is common between the two triangles RC = QC = l.

Repeat the same procedure and we find out that perimeter of quadrangle ABCD = 2k + 2l + 2m + 2n = 2(k + n + m + l) = 2(AB + CD).

So statement 1 by itself is sufficient.

St2 --> m + l = 5. Clearly insufficient as we do not know the value of k + n.

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Re: What is the perimeter of quadrangle ABCD in which a circle is inscribe  [#permalink]

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29 Nov 2019, 18:59
Bunuel wrote:

What is the perimeter of quadrangle ABCD in which a circle is inscribed?

(1) AB + DC = 8
(2) BC = 5

Attachment:
untitled.JPG

If you want to understand the underlying concept in this problem, search for the Pitot theorem.

According to the Pitot theorem, the sum of pairs of opposite sides is the same.

Statement 1 is sufficient to answer the question. Statement 2 does not answer the question on its own.
Hence, Answer choice A is correct.
Re: What is the perimeter of quadrangle ABCD in which a circle is inscribe   [#permalink] 29 Nov 2019, 18:59
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