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19 May 2021, 03:00
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A
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Difficulty:
95%
(hard)
Question Stats:
18% (01:59) correct
82%
(02:28)
wrong
based on 44
sessions
History
Date
Time
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Not Attempted Yet
Circle P above circumscribes rectangle ABCD. What is the value of w°+x°+y°+z°?
(1) ABCD is a square.
(2) EF is a diameter of the circle P.
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22 May 2021, 02:45
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Circle P above circumscribes rectangle ABCD. What is the value of w°+x°+y°+z°?
(1) ABCD is a square.
The Central Angle Theorem states that the measure of inscribed angle is always half the measure of the central angle.
So the central angle which subtends the minor arc BC equals to twice the angle x+z (as inscribed angle x plus inscribed angle z subtend the same minor arc BC). Now, minor arc BC is 1/4 of the circumference (because ABCD is a square) hence the central angle which subtends it equals to 360/4=90 --> 90=2(x+z) --> x+z=45;
Similarly 90=2(w+y) (for minor arc AD) --> w+y=45;
x+z+w+y=90.
Sufficient.
(2) EF is a diameter of the circle P. By squeezing/stretching AD the value of w°+x°+y°+z° changes, thus we cannot get the single value. Not sufficient.
Answer: A.
General Discussion
RamseyGooner
Current Student
Joined: 29 Feb 2020
Last visit: 03 Oct 2022
Posts: 53
Own Kudos:
Given Kudos: 56
Location: India
Schools: Said '23 (A) Judge '23 (WA) Bocconi (A$$) ESSEC (A)
GMAT 1: 720 Q49 V40
GPA: 3.5
Schools: Said '23 (A) Judge '23 (WA) Bocconi (A$$) ESSEC (A)
GMAT 1: 720 Q49 V40
Posts: 53
Kudos:
54
27 May 2021, 04:46
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Pl help Bunuel chetan2u
I am unable to understand this concept "So the central angle which subtends the minor arc BC equals to twice the angle x+z (as inscribed angle x plus inscribed angle z subtend the same minor arc BC)"
How does z subtend to the same minor arc BC? Furthemore, i could understand that x = 22.5 if it were given that EF is the angle bisector of angle BEC but that is not the case.
Would appreciate if any one could bridge the gap in my thinking.
Thanks,
R
I am unable to understand this concept "So the central angle which subtends the minor arc BC equals to twice the angle x+z (as inscribed angle x plus inscribed angle z subtend the same minor arc BC)"
How does z subtend to the same minor arc BC? Furthemore, i could understand that x = 22.5 if it were given that EF is the angle bisector of angle BEC but that is not the case.
Would appreciate if any one could bridge the gap in my thinking.
Thanks,
R
