Oct 20 07:00 AM PDT  09:00 AM PDT Get personalized insights on how to achieve your Target Quant Score. Oct 22 09:00 AM PDT  10:00 AM PDT Watch & learn the Do's and Don’ts for your upcoming interview Oct 22 08:00 PM PDT  09:00 PM PDT On Demand for $79. For a score of 4951 (from current actual score of 40+) AllInOne Standard & 700+ Level Questions (150 questions) Oct 23 08:00 AM PDT  09:00 AM PDT Join an exclusive interview with the people behind the test. If you're taking the GMAT, this is a webinar you cannot afford to miss! Oct 26 07:00 AM PDT  09:00 AM PDT Want to score 90 percentile or higher on GMAT CR? Attend this free webinar to learn how to prethink assumptions and solve the most challenging questions in less than 2 minutes. Oct 27 07:00 AM EDT  09:00 AM PDT Exclusive offer! Get 400+ Practice Questions, 25 Video lessons and 6+ Webinars for FREE. Oct 27 08:00 PM EDT  09:00 PM EDT Strategies and techniques for approaching featured GMAT topics. One hour of live, online instruction
Author 
Message 
TAGS:

Hide Tags

eGMAT Representative
Joined: 04 Jan 2015
Posts: 3078

AB and CD are two parallel chords of a circle, with center O .........
[#permalink]
Show Tags
05 Dec 2018, 01:11
Question Stats:
77% (02:15) correct 23% (02:47) wrong based on 93 sessions
HideShow timer Statistics
AB and CD are two parallel chords of a circle, with center O, such that AB = 12 and CD = 6. If the diameter of the circle is 6√5, then find the distance between the two chords?
Official Answer and Stats are available only to registered users. Register/ Login.
_________________



NUS School Moderator
Joined: 18 Jul 2018
Posts: 1021
Location: India
Concentration: Finance, Marketing
WE: Engineering (Energy and Utilities)

AB and CD are two parallel chords of a circle, with center O .........
[#permalink]
Show Tags
05 Dec 2018, 02:08
OA = radius = \(6\sqrt{5}/2\) = \(3\sqrt{5}\) = OD From the attached below image. AE = 6. CF = 3. Then OE as per Pythagorean theorem gives \(\sqrt{4536}\) = 3. OF = \(\sqrt{459}\)= 6. OF = OE + EF EF = 63 = 3. B is the answer.
Attachments
ps1.png [ 7.86 KiB  Viewed 1232 times ]
_________________
Press +1 Kudos If my post helps!



eGMAT Representative
Joined: 04 Jan 2015
Posts: 3078

AB and CD are two parallel chords of a circle, with center O .........
[#permalink]
Show Tags
10 Dec 2018, 02:01
Solution Given:We are given that, • AB and CD are two parallel chords of a circle • O is the center of the circle • AB = 12 and CD = 6 • Diameter of the circle = 6√5 To find:• The distance between the two chords, AB and CD Approach and Working: From the above figure, we can infer that we need to find the value of EF In triangle, OAE, we know that, • \(AE = \frac{AB}{2} = \frac{12}{2} = 6\) • OA = radius of the circle =\(\frac{6√5}{2} = 3√5\) • \(∠OEA = 90^o\) So, we can write, \(OA^2 = OE^2 + AE^2\) • Implies, \((3√5)^2 = OE^2 + 6^2\) • \(OE^2 = 45 – 36 = 9\) • Thus, OE = √9 = 3
Similarly, in triangle DOF, we ca say that • \(OD^2 = OF^2 + FD^2\)
o \((3√5)^2 = OF^2 + (\frac{6}{2})^2\) o \(OF^2 = 45 – 9 = 36\) • Thus, OF = √36 = 6 Therefore, EF = OF = OE = 6 – 3 = 3 Hence the correct answer is Option B. Answer: B
_________________



Senior Manager
Joined: 13 Feb 2018
Posts: 450

Re: AB and CD are two parallel chords of a circle, with center O .........
[#permalink]
Show Tags
22 Jan 2019, 05:34
EgmatQuantExpertPlease explain a bit more why AE=EB Regards L



eGMAT Representative
Joined: 04 Jan 2015
Posts: 3078

Re: AB and CD are two parallel chords of a circle, with center O .........
[#permalink]
Show Tags
22 Jan 2019, 23:38
LevanKhukhunashvili wrote: EgmatQuantExpertPlease explain a bit more why AE=EB Regards L Hi, If you see the two triangles AOE and EOB, both are congruent triangles. AO = OB = radius, OE is a common side, and angle OEA = angle OEB = 90 degrees Thus, the length of the third sides must be equal, that is, AE = EB Regards,
_________________




Re: AB and CD are two parallel chords of a circle, with center O .........
[#permalink]
22 Jan 2019, 23:38






