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

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

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New post 29 Jul 2016, 03:00
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A
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Question Stats:

35% (01:24) correct 65% (01:49) wrong based on 132 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

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

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New post 29 Jul 2016, 08:29
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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New post 02 Nov 2016, 14:53
Can someone please explain this? I don't understand the underlying concept.

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

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New post 03 Nov 2016, 06:54
lawiniecke wrote:
Can someone please explain this? I don't understand the underlying concept.

Thanks in advance! :)


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.

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

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New post 03 Nov 2016, 21:39
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Bunuel wrote:
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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:
The attachment untitled.JPG is no longer available


Please check the detailed explanation in the attached picture

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

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New post 22 Feb 2018, 02:27
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Re: What is the perimeter of quadrangle ABCD in which a circle is inscribe &nbs [#permalink] 22 Feb 2018, 02:27
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