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705-805 (Hard)|   Geometry|      
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What is the perimeter of quadrangle ABCD in which a circle is inscribe 29 Jul 2016, 04:00
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A
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85% (hard)

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33% (01:30) correct 67% (01:49) wrong based on 186 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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What is the perimeter of quadrangle ABCD in which a circle is inscribe 03 Nov 2016, 22:39
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Bunuel

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

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

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Please check the detailed explanation in the attached picture

Answer: Option A
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kshitij ghildiyal
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What is the perimeter of quadrangle ABCD in which a circle is inscribe 29 Jul 2016, 09:29
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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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What is the perimeter of quadrangle ABCD in which a circle is inscribe 02 Nov 2016, 15:53
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Can someone please explain this? I don't understand the underlying concept.

Thanks in advance! :)
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What is the perimeter of quadrangle ABCD in which a circle is inscribe 03 Nov 2016, 07:54
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lawiniecke
Can someone please explain this? I don't understand the underlying concept.

Thanks in advance! :)
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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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What is the perimeter of quadrangle ABCD in which a circle is inscribe 29 Nov 2019, 18:59
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Bunuel

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

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

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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.

Therefore, AB+CD= BC+AD.
Statement 1 is sufficient to answer the question. Statement 2 does not answer the question on its own.
Hence, Answer choice A is correct.
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What is the perimeter of quadrangle ABCD in which a circle is inscribe 06 Feb 2020, 21:07
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