January 26, 2019 January 26, 2019 07:00 AM PST 09:00 AM PST Attend this webinar to learn how to leverage Meaning and Logic to solve the most challenging Sentence Correction Questions. January 27, 2019 January 27, 2019 07:00 AM PST 09:00 AM PST Attend this webinar to learn a structured approach to solve 700+ Number Properties question in less than 2 minutes.
Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 52431

In the figure shown, quadrilateral ABCD is inscribed in a circle of
[#permalink]
Show Tags
03 Jul 2016, 09:51
Question Stats:
72% (01:13) correct 28% (01:18) wrong based on 829 sessions
HideShow timer Statistics




SC Moderator
Joined: 13 Apr 2015
Posts: 1687
Location: India
Concentration: Strategy, General Management
GPA: 4
WE: Analyst (Retail)

In the figure shown, quadrilateral ABCD is inscribed in a circle of
[#permalink]
Show Tags
03 Jul 2016, 10:11
Given: Radius = 5 Perimeter of ABCD = AB + BC + CD + AD = ?
St1: The length of AB is 6 and the length of CD is 8. > AB = 6 and CD = 8 Not Sufficient as value of BC and AD is not known.
St2: AC = diameter = 10 > ABC and ADC are right angled triangles. Values of the sides of the quadrilateral cannot be derived. Insufficient
Combining St1 and St2: AB = 6, CD = 8, ABC and ADC are right angled triangles In ABC, AC = 10, AB = 6 > BC = sqrt(10^2  6^2) = 8 In ADC, AC = 10, CD = 8 > AD = sqrt(10^2  8^2) = 6 Perimeter = AB + BC + CD + AD = 28 Sufficient
Answer: C




Senior Manager
Joined: 02 Mar 2012
Posts: 301

In the figure shown, quadrilateral ABCD is inscribed in a circle of
[#permalink]
Show Tags
Updated on: 04 Jul 2016, 19:25
we need 2 imp info
1)ac is diamter 2)ac is perpendicular to BD
combining both we don't know AC is perpndclr to BD
SO C
we can find the lengths from pythagorus theorem.
Originally posted by hsbinfy on 03 Jul 2016, 22:29.
Last edited by hsbinfy on 04 Jul 2016, 19:25, edited 1 time in total.



Senior Manager
Joined: 02 Mar 2012
Posts: 301

In the figure shown, quadrilateral ABCD is inscribed in a circle of
[#permalink]
Show Tags
03 Jul 2016, 22:40
Vyshak wrote: Given: Radius = 5 Perimeter of ABCD = AB + BC + CD + AD = ?
St1: The length of AB is 6 and the length of CD is 8. > AB = 6 and CD = 8 Not Sufficient as value of BC and AD is not known.
St2: AC = diameter > We can infer that AC bisects line segment BD Let O be the point of intersection of AC and BD. Triangles AOD and AOB are congruent > Therefore AB = AD Triangles COB and COD are congruent > Therefore BC = CD AC = 10 Not Sufficient to determine the perimeter
Combining St1 and St2: Perimeter = AB + BC + CD + AD = 2(AB + CD) = 2(6 + 8) = 28 Sufficient
Answer: C St2: AC = diameter > We can infer that AC bisects line segment BD how can you infer above statement until it is given AC is perpendicular to BD? it will only bisect if AC is perpendicular to BD OR AC and BD intersect at centre of circle



SC Moderator
Joined: 13 Apr 2015
Posts: 1687
Location: India
Concentration: Strategy, General Management
GPA: 4
WE: Analyst (Retail)

Re: In the figure shown, quadrilateral ABCD is inscribed in a circle of
[#permalink]
Show Tags
03 Jul 2016, 23:33
hsbinfy wrote: Vyshak wrote: Given: Radius = 5 Perimeter of ABCD = AB + BC + CD + AD = ?
St1: The length of AB is 6 and the length of CD is 8. > AB = 6 and CD = 8 Not Sufficient as value of BC and AD is not known.
St2: AC = diameter > We can infer that AC bisects line segment BD Let O be the point of intersection of AC and BD. Triangles AOD and AOB are congruent > Therefore AB = AD Triangles COB and COD are congruent > Therefore BC = CD AC = 10 Not Sufficient to determine the perimeter
Combining St1 and St2: Perimeter = AB + BC + CD + AD = 2(AB + CD) = 2(6 + 8) = 28 Sufficient
Answer: C St2: AC = diameter > We can infer that AC bisects line segment BD how can you infer above statement until it is given AC is perpendicular to BD? it will only bisect if AC is perpendicular to BD OR AC and BD intersect at centre of circle Yes we cannot infer from Statement 2 that the two triangles are congruent. Thanks for spotting it. But the answer is still C. Since AC is the diameter, ABC and ADC are right angled. In ABC, AC = 10, AB = 6 > BC = sqrt(10^2  6^2) = 8 In ADC, AC = 10, CD = 8 > AD = sqrt(10^2  8^2) = 6 Perimeter of the triangle = 6 + 8 + 6 + 8 = 28.



Manager
Joined: 17 Nov 2014
Posts: 51
Location: India

Re: In the figure shown, quadrilateral ABCD is inscribed in a circle of
[#permalink]
Show Tags
10 Jul 2016, 06:36
Given: Radius of Circle = 5 Perimeter of ABCD AB + BC + CD + AD = ?
Statement 1: The length of AB is 6 and the length of CD is 8. > AB = 6 and CD = 8 Not Sufficient, since the value of BC and AD is not known.
Statement 2: AC = diameter = 10 > ABC and ADC are right angled triangles. Values of the sides of the quadrilateral cannot be derived. Insufficient
Combining St1 and St2: AB = 6, CD = 8, ABC and ADC are right angled triangles Perimeter can be derived.
Sample Calculation: ABC right angle triangle, AC =10, AB = 6 \(BC^2 = AC^2  AB^2\) BC = 8
Answer: C



Director
Status: I don't stop when I'm Tired,I stop when I'm done
Joined: 11 May 2014
Posts: 534
Location: Bangladesh
Concentration: Finance, Leadership
GPA: 2.81
WE: Business Development (Real Estate)

In the figure shown, quadrilateral ABCD is inscribed in a circle of
[#permalink]
Show Tags
10 Jul 2016, 18:04
In the figure shown, quadrilateral ABCD is inscribed in a circle of radius 5. What is the perimeter of quadrilateral ABCD? (1) The length of AB is 6 and the length of CD is 8......>no information about the lengths of other two sides(information required because we don't know which specific quadrilateral is quadrilateral ABCD above), Insufficient(2) AC is a diameter of the circle.........>So now we know AC=10 and its opposite angle \(\angle\)ABC=\(90^{\circ}\)(for \(\triangle\) ABC) and \(\angle\)ADC=\(90^{\circ}\)(for \(\triangle\) ADC),But still we don know the lengths of any sides of the Quadrilateral ABCD, Insufficient(1)+(2) AB=6,AC=10 and \(\angle\)ABC=\(90^{\circ}\) so According to pythagorean triple BC=\(\sqrt{AC^2+AB^2}\)=\(\sqrt{10^26^2}\)=8 Accordingly we can find AD=6 So,perimeter of quadrilateral ABCD=AB+BC+CD+AD=6+8+8+6=28, SufficientCorrect Answer C
_________________
Md. Abdur Rakib
Please Press +1 Kudos,If it helps Sentence CorrectionCollection of Ron Purewal's "elliptical construction/analogies" for SC Challenges



Board of Directors
Joined: 17 Jul 2014
Posts: 2598
Location: United States (IL)
Concentration: Finance, Economics
GPA: 3.92
WE: General Management (Transportation)

Re: In the figure shown, quadrilateral ABCD is inscribed in a circle of
[#permalink]
Show Tags
27 Apr 2017, 14:40
each alone is not sufficient. 1+2 => we have 2 right triangles (properties of inscribed triangles in a circle, where the hypotenuse is the diameter). we know 2 sides, we can find 3rd side for each triangle. in the end, we can find the perimeter.



Intern
Joined: 14 Nov 2015
Posts: 37
Location: India
GPA: 3.7

Re: In the figure shown, quadrilateral ABCD is inscribed in a circle of
[#permalink]
Show Tags
29 Sep 2017, 04:47
Hi,
A quadrilateral inside a cirlce is called a cyclic quadrilateral.
And one of the properties of a cyclic quadrilateral is AB + CD = AD + BC (based on given fig.)
So shouldn't A be the answer choice?
Can someone explain pl.
Thanks



Math Expert
Joined: 02 Sep 2009
Posts: 52431

Re: In the figure shown, quadrilateral ABCD is inscribed in a circle of
[#permalink]
Show Tags
29 Sep 2017, 05:14



Intern
Joined: 30 Oct 2014
Posts: 14

Re: In the figure shown, quadrilateral ABCD is inscribed in a circle of
[#permalink]
Show Tags
06 Dec 2017, 04:21
(1) is very easily insuff but...
If we know that AC is the diameter of the circle and thus = 10, why wouldn't we say suff for (2) just off of the Pythagorean triplet 6810?
That would tell me that AB/AD = 6 and BC/DC = 8.
6+6+8+8 = 28



DS Forum Moderator
Joined: 21 Aug 2013
Posts: 1435
Location: India

Re: In the figure shown, quadrilateral ABCD is inscribed in a circle of
[#permalink]
Show Tags
06 Dec 2017, 22:38
Roosterbooster wrote: (1) is very easily insuff but...
If we know that AC is the diameter of the circle and thus = 10, why wouldn't we say suff for (2) just off of the Pythagorean triplet 6810?
That would tell me that AB/AD = 6 and BC/DC = 8.
6+6+8+8 = 28 Hi Based on statement 2, yes we know that both ABC and ADC are right angle triangles with hypotenuse AC=10. But we cannot just assume that a right angle triangle with hypotenuse 10 will only be a 6810 triangle. It could also be 5√25√210 triangle OR it could be 2√54√510 triangle. Only if we are given that its a right angle triangle with hypotenuse 10 and one side 6 (or 8), then we can conclude that the third side would be 8 (or 6). Or if we are given that all sides are integers and hypotenuse is 10, can we conclude that the other two sides (legs) would be 6/8.



Intern
Joined: 19 May 2018
Posts: 12

Re: In the figure shown, quadrilateral ABCD is inscribed in a circle of
[#permalink]
Show Tags
07 Jun 2018, 13:09
So, the takeawayproperty would be the ThalesTheorem...?



Manager
Joined: 18 Apr 2018
Posts: 98

In the figure shown, quadrilateral ABCD is inscribed in a circle of
[#permalink]
Show Tags
04 Oct 2018, 04:23
Vyshak wrote: Given: Radius = 5 Perimeter of ABCD = AB + BC + CD + AD = ?
St1: The length of AB is 6 and the length of CD is 8. > AB = 6 and CD = 8 Not Sufficient as value of BC and AD is not known.
St2: AC = diameter = 10 > ABC and ADC are right angled triangles. Values of the sides of the quadrilateral cannot be derived. Insufficient
Combining St1 and St2: AB = 6, CD = 8, ABC and ADC are right angled triangles In ABC, AC = 10, AB = 6 > BC = sqrt(10^2  6^2) = 8 In ADC, AC = 10, CD = 8 > AD = sqrt(10^2  8^2) = 6 Perimeter = AB + BC + CD + AD = 28 Sufficient
Answer: C Hello, Vyshakthanks so much for this wholesome explanation but I don't still understand why you assumed BC=CD, is this a specific property or just because they look the same in the figure? Thanks. Posted from my mobile device



Manager
Joined: 13 Aug 2018
Posts: 62

Re: In the figure shown, quadrilateral ABCD is inscribed in a circle of
[#permalink]
Show Tags
16 Oct 2018, 20:24
Bunuel wrote: In the figure shown, quadrilateral ABCD is inscribed in a circle of radius 5. What is the perimeter of quadrilateral ABCD? (1) The length of AB is 6 and the length of CD is 8. (2) AC is a diameter of the circle. Attachment: 20160703_2149.png I don't understand how we can take triangle ABC and ACD as a right angle triangle after the (1) and (2) statement. Please help.. Thanks



Manager
Joined: 28 Jun 2018
Posts: 74

Re: In the figure shown, quadrilateral ABCD is inscribed in a circle of
[#permalink]
Show Tags
16 Nov 2018, 04:36
Hello,
Wondering we need 2 at all? Doesn't inscribed mean that the points touch the ends of the circle? Which means its the diameter anyway??



DS Forum Moderator
Joined: 21 Aug 2013
Posts: 1435
Location: India

Re: In the figure shown, quadrilateral ABCD is inscribed in a circle of
[#permalink]
Show Tags
18 Nov 2018, 03:51
hibobotamuss wrote: Hello,
Wondering we need 2 at all? Doesn't inscribed mean that the points touch the ends of the circle? Which means its the diameter anyway?? Hello Yes, inscribed means that all the points touch the ends of the circle. But that doesnt necessarily mean that AC is diameter only. AC and BD are the diagonals of this quadrilateral, but its quite possible that none of those two diagonals pass through the center of the circle. Thats why second statement is needed.



Manager
Joined: 28 Jun 2018
Posts: 74

Re: In the figure shown, quadrilateral ABCD is inscribed in a circle of
[#permalink]
Show Tags
18 Nov 2018, 04:06
Aahhhhhhh, makes sense. Didn't think of that :/




Re: In the figure shown, quadrilateral ABCD is inscribed in a circle of &nbs
[#permalink]
18 Nov 2018, 04:06






