gmatblood wrote:Please help to answer this question.
IMO B
OA?
ARC
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vaibhavgupta
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IMO B
OA?
If OA is A, IMO B
If OA is B, IMO C
If OA is C, IMO D
If OA is D, IMO E
If OA is E, IMO A
FML!! :/
If OA is B, IMO C
If OA is C, IMO D
If OA is D, IMO E
If OA is E, IMO A
FML!! :/
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Anurag@Gurome
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Length of arc AXB = 2*(Length of arc BZC)
Length of arc AYC = 3*(Length of arc AXB) = 6*(Length of arc BZC)
Hence, circumference of the circle = (Length of arc AXB) + (Length of arc BZC) + (Length of arc AYC) = (1 + 2 + 6)*(Length of arc BZC) = 9*(Length of arc BZC) = (9/2)*(Length of arc AXB)
Now circumference of the circle subtends an angle of 360° in the center of the circle. Say, arc AXB subtends an angle of x° in the center.
Then, (9/2)*(Length of arc AXB) subtends an angle of 360° in the center of the circle.
So, length of arc AXB will subtend an angle of (2/9)*360° = 80° in the center of the circle.
Now, measure of angle BCA = half of the measure of the angle subtended by arc AXB in the center of the circle = 40°
The correct answer is B.
Length of arc AYC = 3*(Length of arc AXB) = 6*(Length of arc BZC)
Hence, circumference of the circle = (Length of arc AXB) + (Length of arc BZC) + (Length of arc AYC) = (1 + 2 + 6)*(Length of arc BZC) = 9*(Length of arc BZC) = (9/2)*(Length of arc AXB)
Now circumference of the circle subtends an angle of 360° in the center of the circle. Say, arc AXB subtends an angle of x° in the center.
Then, (9/2)*(Length of arc AXB) subtends an angle of 360° in the center of the circle.
So, length of arc AXB will subtend an angle of (2/9)*360° = 80° in the center of the circle.
Now, measure of angle BCA = half of the measure of the angle subtended by arc AXB in the center of the circle = 40°
The correct answer is B.
Anurag Mairal, Ph.D., MBA
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rijul007
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From the figure above :
Angle A = a
Angle B = b
Angle C = c
Circumference of thecircle = m
AXB = x = (2c/360) * m
BZC = z = (2a/360) * m
CYA = y = (2b/360) * m
x = 2z
2c = 2(2a)
c= 2a
y = 3x
2b = 3(2c)
b = 3c
2a + 2b + 2c = 360
a+b+c = 180
c/2 + 3c + c = 180
9c/2 = 180
c = 40
Option B
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gmatblood
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Could you please elaborate on the last part of the solution!Anurag@Gurome wrote:Length of arc AXB = 2*(Length of arc BZC)
Length of arc AYC = 3*(Length of arc AXB) = 6*(Length of arc BZC)
Hence, circumference of the circle = (Length of arc AXB) + (Length of arc BZC) + (Length of arc AYC) = (1 + 2 + 6)*(Length of arc BZC) = 9*(Length of arc BZC) = (9/2)*(Length of arc AXB)
Now circumference of the circle subtends an angle of 360° in the center of the circle. Say, arc AXB subtends an angle of x° in the center.
Then, (9/2)*(Length of arc AXB) subtends an angle of 360° in the center of the circle.
So, length of arc AXB will subtend an angle of (2/9)*360° = 80° in the center of the circle.
Now, measure of angle BCA = half of the measure of the angle subtended by arc AXB in the center of the circle = 40°
The correct answer is B.
Thanks
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Anurag@Gurome
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There is a theorem which says, the angle at the center of a circle is twice the angle at the circumference if both angles stand on the same arc.
For proof, have a look at the middle of the following webpage with a heading "Angle at the Center" : https://www.mathsrevision.net/gcse/pages.php?page=13
Hence, measure of angle BCA = half of the measure of the angle subtended by arc AXB in the center of the circle as they both stand on the same arc, i.e. AXB
For proof, have a look at the middle of the following webpage with a heading "Angle at the Center" : https://www.mathsrevision.net/gcse/pages.php?page=13
Hence, measure of angle BCA = half of the measure of the angle subtended by arc AXB in the center of the circle as they both stand on the same arc, i.e. AXB
Anurag Mairal, Ph.D., MBA
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