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The circle above is circumscribed around square ABCD. Points E and F

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Bunuel
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The circle above is circumscribed around square ABCD. Points E and F [#permalink] New post   12 May 2021, 01:30
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The circle above is circumscribed around square ABCD. Points E and F lie on minor arcs AB and CD respectively. The measure of minor arc EF is between

A. 90° and 270°
B. 90° and 180°
C. 60° and 120°
D. 0° and 90°
E. 0° and 180°



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Re: The circle above is circumscribed around square ABCD. Points E and F [#permalink] New post   12 May 2021, 02:28
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Bunuel wrote:

The circle above is circumscribed around square ABCD. Points E and F lie on minor arcs AB and CD respectively. The measure of minor arc EF is between

A. 90° and 270°
B. 90° and 180°
C. 60° and 120°
D. 0° and 90°
E. 0° and 180°



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The angle is minimised when E overlaps with A and F overlaps with D.

Assuming O as the center of the circle (and also the square), angle EOD = 90 degree

The maximum angle is when EOD forms a straight line, ie becomes the diameter; angle EOD equals 180 degree

Thus, the angle lies between 90 and 180

Answer B

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Re: The circle above is circumscribed around square ABCD. Points E and F [#permalink] New post   12 May 2021, 04:29
The measure of angle at center of the circle will be least when AD lies on E and F respectively i.e 90 degree and mximum when E and F will be in a straight line i.e 180 degree
B is the right answer IMO
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Re: The circle above is circumscribed around square ABCD. Points E and F [#permalink] New post   12 May 2021, 06:28
E and F can coincide with A and D points respectively.
So, min. angle form by minor arc EF = Angle formed at center by diagonals of square =90

And at max position E and F can be at diameter position, so max. angle form by minor arc EF =180

So, I think B. :)
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Re: The circle above is circumscribed around square ABCD. Points E and F [#permalink] New post   12 May 2021, 18:23
Bunuel wrote:

The circle above is circumscribed around square ABCD. Points E and F lie on minor arcs AB and CD respectively. The measure of minor arc EF is between
A. 90° and 270°
B. 90° and 180°
C. 60° and 120°
D. 0° and 90°
E. 0° and 180°


We have to find the min and max measure of the minor arc EF.

At minimum measure for the minor arc, E and F coincide with A and D respectively.
As the points coincide with one side of a square, the measure of the arc EF here is 90°

At maximum measure for the minor arc, E and F are exactly opposite each other, such that a diameter line can be drawn between them.
In such a case, the measure of the arc EF here is 180°

Answer should be Option B.
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Re: The circle above is circumscribed around square ABCD. Points E and F [#permalink]
12 May 2021, 18:23
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