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If O is the center of the circle shown above and BC=CD, what is the va [#permalink]
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22 Sep 2016, 05:09
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Re: If O is the center of the circle shown above and BC=CD, what is the va [#permalink]
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22 Sep 2016, 05:20
Is the answer 20? Sorry Bunuel, I cannot see the answer since I am using the mobile app Sent from my iPhone using GMAT Club Forum mobile app



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Re: If O is the center of the circle shown above and BC=CD, what is the va [#permalink]
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22 Sep 2016, 05:25



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Re: If O is the center of the circle shown above and BC=CD, what is the va [#permalink]
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22 Sep 2016, 06:05
I have opted for 20 deg.



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Re: If O is the center of the circle shown above and BC=CD, what is the va [#permalink]
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22 Sep 2016, 11:27
Opting for 20 degrees.



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Re: If O is the center of the circle shown above and BC=CD, what is the va [#permalink]
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22 Sep 2016, 13:35
I got the answer 20 but had a question for clarification. We know that ACD is 90 but we cannot assume ABC is also 90 since AC and AD are different lengths. Based on my calculations I got CAB = 20, ABC = 110 and BCA = 50. Wanted to know if this was the correct process.
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Re: If O is the center of the circle shown above and BC=CD, what is the va [#permalink]
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22 Sep 2016, 14:03
How do we know that ACD is 90 degrees?



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If O is the center of the circle shown above and BC=CD, what is the va [#permalink]
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22 Sep 2016, 16:09
joannaecohen wrote: How do we know that ACD is 90 degrees? A triangle inscribed in a circle who hypotenuse is the diameter of the circle forms a 90 degree angle at the circumference.



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Re: If O is the center of the circle shown above and BC=CD, what is the va [#permalink]
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22 Sep 2016, 22:05
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Bunuel wrote: If O is the center of the circle shown above and BC=CD, what is the value of x? A. 15° B. 20° C. 25° D. 30° E. 40° This is a tricky question. We have hidden arc and angle information and we can find the angle information via arc. ( NOTE : Arc angle is double the center angle ) ACD is a right angled triangle. we have C = 90 , D (given) = 70 and thus A is 20. When we have angle A 20 degrees and the arc under CD is 40. We are given that BC = CD...i.e. arc under BC is also 40 degrees and finally x is 20. IMO option B.



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Re: If O is the center of the circle shown above and BC=CD, what is the va [#permalink]
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22 Sep 2016, 22:30
ACD=90 Hence CAD=20
also ABC=110 as opp angles of a cyclic quad are supplementary.
join BD ABD=90 DBC=ABCABD=11090=20
In triangle BCD, CBD=CDB=20
hence BDA=50
now in triangle ABD ABD=90, BDA=50, BAD=x+20 hence x=20
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Re: If O is the center of the circle shown above and BC=CD, what is the va [#permalink]
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23 Sep 2016, 01:28
In ΔACD, ∠ACD is an inscribed angle intercepting the diameter of the circle and is therefore 90°. ∠CAD=180(70+90)=20°. Hence, minor arc CD is 40°. Minor arcs BC and CD lie on identical chords and are therefore equal. Thus, minor arc BC is 40°, and x=20°



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Re: If O is the center of the circle shown above and BC=CD, what is the va [#permalink]
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23 Sep 2016, 04:12
Harish Yannam wrote: In ΔACD, ∠ACD is an inscribed angle intercepting the diameter of the circle and is therefore 90°. ∠CAD=180(70+90)=20°. Hence, minor arc CD is 40°. Minor arcs BC and CD lie on identical chords and are therefore equal. Thus, minor arc BC is 40°, and x=20° this file will explain visually i hope it helps Answer is B 20°
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1.png [ 22.33 KiB  Viewed 991 times ]



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Re: If O is the center of the circle shown above and BC=CD, what is the va [#permalink]
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24 Sep 2016, 02:54
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From the attached diagram, Inscribed angle is half of central angle. Hence \(BAC = 1/2*BOC\) Likewise \(CAD = 1/2*COD\) Also since \(BC = CD\), arc BC = arc CD => \(BOC = COD\) therefore \(BAC = CAD\) that is \(X = Y\) Now \(OC = OD\) hence \(OCD = ODC\) => \(COD = 40\) thus \(X = 20\)
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Re: If O is the center of the circle shown above and BC=CD, what is the va [#permalink]
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18 Sep 2017, 03:15
azamaka wrote: Harish Yannam wrote: In ΔACD, ∠ACD is an inscribed angle intercepting the diameter of the circle and is therefore 90°. ∠CAD=180(70+90)=20°. Hence, minor arc CD is 40°. Minor arcs BC and CD lie on identical chords and are therefore equal. Thus, minor arc BC is 40°, and x=20° this file will explain visually i hope it helps Answer is B 20°Hi, seems to be a good solution, but I have a questionHow can we say that AB=BD in order to get both the green angles as 45 deg? Thanx




Re: If O is the center of the circle shown above and BC=CD, what is the va
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