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AB or AE : Quantitative Comparison Questions

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Re: AB or AE [#permalink]
Carcass wrote:
Attachment:
circle.jpg


Quantity A
Quantity B
\(\widehat{AB}\)
\(\widehat{AE}\)


A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.

Can anyone help me with the solution? I think it has something to do with inscribed angles? please help me out!!!
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Re: AB or AE [#permalink]
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Shad1968 wrote:
Carcass wrote:
Attachment:
circle.jpg


Quantity A
Quantity B
\(\widehat{AB}\)
\(\widehat{AE}\)


A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.

Can anyone help me with the solution? I think it has something to do with inscribed angles? please help me out!!!


I think the point C is not mentioned as the centre hence we cannot proceed therefore the answer is D
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Re: AB or AE [#permalink]
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So. Here goes my best answer.
Segments AD and EB are both diameters.
since Two diameters can only intersect at the center, then the intersections happen at right angles.
Thus, Angle C is 90 degrees.
segment AB is opposite angle C,
since any angle at the intersection of the circle is also 90 degrees, then any segment opposite any of those angles will be the same length as AB.
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Re: AB or AE [#permalink]
Expert Reply
chetan2u wrote:
HappyMathtutor wrote:
So. Here goes my best answer.
Segments AD and EB are both diameters.
since Two diameters can only intersect at the center, then the intersections happen at right angles.
Thus, Angle C is 90 degrees.
segment AB is opposite angle C,
since any angle at the intersection of the circle is also 90 degrees, then any segment opposite any of those angles will be the same length as AB.



You are wrong on two points..
(1) It is nowhere given AD and EB are the diameters.
(2) even if they were the diameters, it is not necessary that the diameters intersect at 90 degree....intersection can be anything from 0 to 180.ONLY perpendicular diameters bisect each other at 90..

Although if AD and EB are diameters, the opposite angles at the intersection will be equal and will result in equal chord.




youre right!!!
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Re: AB or AE [#permalink]
Explanation of the solution to this question would be greatly appreciated.
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Re: AB or AE [#permalink]
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This question, actually, does not need any kind of calculation. Only a good evaluation and observation up-front.

Inside the triangle ECD, you only do know that one angle is 40°. You do not know the other two angles. Therefore, the angle D could be smaller and the inclination of segment AE is less. The result is that AE is narrower and AE < AB. And Vice-versa.

Hope this helps.

Regards
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Re: AB or AE [#permalink]
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Carcass wrote:
Attachment:
circle.jpg


Quantity A
Quantity B
\(\widehat{AB}\)
\(\widehat{AE}\)


A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.

If the question says 'C' is the center, then we can go further otherwise here clear 'D'.
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Re: AB or AE [#permalink]
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Since we're not told if C is or is not the center of the circle, we can't infer anything about the arcs regardless of what we determine about the angles that are part of the figure portrayed within the circle.
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Re: AB or AE [#permalink]
The answer is D because you don't know if point C is the center of the circle or not. Because of this, you don't know if lines CE or CD is the radius and without that, the solution cannot be determined.
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Re: AB or AE [#permalink]
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