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Circle segmented into three parts. Two parallel chords thro 29 Aug 2009, 17:12
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Circle segmented into three parts. Two parallel chords through the circle. Chords lengths are 2 SqaureRoot 2 each with a distance of 2 SquareRoot 2 away from each other in the circle. What is the area of each segment?

I'll attach a picture.

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Circle segmented into three parts. Two parallel chords thro 29 Aug 2009, 18:22
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1. Draw a square.
2. Diagonal of the square = sqrt( 4*2 + 4*2) = 4
3. Diagonal of the square = diameter of circle = 4
4. Radius of the circle = 2
5. Area of circle = 4*pi
6. Area of square = 2 sqrt(2) * 2 sqrt(2) = 2*4 = 8
7. After you draw a square, area of top/bottom/left/right pieces is ({area of circle} - {area of square} )/4 = (4*pi - 8)/4 = pi - 2

Answer is: pi-2, 8 + 2*(pi-2), pi-2
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Circle segmented into three parts. Two parallel chords thro 29 Aug 2009, 23:09
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Awesome! Thanks. It all makes perfect sense.
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Circle segmented into three parts. Two parallel chords thro 02 May 2011, 00:33
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Area will be slightly greater than pi/5 + 4.Considering the sum of all the 3 segments.
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Circle segmented into three parts. Two parallel chords thro 19 Oct 2013, 22:09
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Bunuel,

The explanation is clear till here-
1. Draw a square.
2. Diagonal of the square = sqrt( 4*2 + 4*2) = 4
3. Diagonal of the square = diameter of circle = 4
4. Radius of the circle = 2
5. Area of circle = 4*pi
6. Area of square = 2 sqrt(2) * 2 sqrt(2) = 2*4 = 8

Can you please solve/explain it further?
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Circle segmented into three parts. Two parallel chords thro 20 Oct 2013, 15:40
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honchos
Bunuel,

The explanation is clear till here-
1. Draw a square.
2. Diagonal of the square = sqrt( 4*2 + 4*2) = 4
3. Diagonal of the square = diameter of circle = 4
4. Radius of the circle = 2
5. Area of circle = 4*pi
6. Area of square = 2 sqrt(2) * 2 sqrt(2) = 2*4 = 8

Can you please solve/explain it further?
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Radius of circle = 2

Area of circle between chords is 4 + 4\sqrt{2}

Area of circle - area of circle between chords = 4pi - (4+4\sqrt{2})
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Circle segmented into three parts. Two parallel chords thro 21 Oct 2013, 01:05
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honchos
Bunuel,

The explanation is clear till here-
1. Draw a square.
2. Diagonal of the square = sqrt( 4*2 + 4*2) = 4
3. Diagonal of the square = diameter of circle = 4
4. Radius of the circle = 2
5. Area of circle = 4*pi
6. Area of square = 2 sqrt(2) * 2 sqrt(2) = 2*4 = 8

Can you please solve/explain it further?
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The idea here is to consider symmetry of the figure. You see the figure inscribed inside a circle is a square, so the left out portions will be divided symmetrically i,e \(\frac{4pi-8}{4}\).

so 2 of these 4 portions belong to the square in the figure(central segment) which is why the central portion is 8+2(pi-2) and other two portions are segment 1 and 2.

the question could have been made tougher if you had a rectangle ,, then you would have to need consider the areas of arcs.

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This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
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