## Poll

8 votes (47.05%) | |||

6 votes (35.29%) | |||

3 votes (17.64%) | |||

2 votes (11.76%) | |||

6 votes (35.29%) | |||

2 votes (11.76%) | |||

3 votes (17.64%) | |||

2 votes (11.76%) | |||

8 votes (47.05%) | |||

6 votes (35.29%) |

**17 members have voted**

In this age of covid, a small group of worshippers don masks and form a prayer circle on the lawn beside their church.

If 8 people stand in a circle with six feet of required social distance between them (along a chord):

1) What is the circumference of the circle?

2) What is the diameter of the circle?

3) How far in a straight line (chord) is Person A from Person C?

4) The prayer circle is formed on a square lawn measuring 25x25 feet. What is the maximum number of people who could stand in the circle and still be 6 feet apart?

Quote:Gialmere

In this age of covid, a small group of worshippers don masks and form a prayer circle on the lawn beside their church.

If 8 people stand in a circle with six feet of required social distance between them (along a chord):

1) What is the circumference of the circle?

2) What is the diameter of the circle?

3) How far in a straight line (chord) is Person A from Person C?

4) The prayer circle is formed on a square lawn measuring 25x25 feet. What is the maximum number of people who could stand in the circle and still be 6 feet apart?

Been a while, so hopefully I'm thinking on the right lines.....

1) C = 49.57ft

2) d = 15.78ft

3) AC cord = 11.15ft (2*7.89) sin(.785 radians)

4) 12 people at most.....if we went to 13 people then we would go slightly over the radius of 12.5.....12.62 would be the radius for 13 people

radius = 3/sin(22.5) = 7.839377789

1. 2*pi*radius = 6*pi/sin(22.5) = 49.2563

2. 2*radius = 6/sin(22.5) = 15.6788

3. sqrt(2)*radius = 3*sqrt(2)/sin(22.5) = 11.0866

If this are right, I'll think about #4.

Quote:Gialmere

In this age of covid, a small group of worshippers don masks and form a prayer circle on the lawn beside their church.

If 8 people stand in a circle with six feet of required social distance between them (along a chord):

1) What is the circumference of the circle?

2) What is the diameter of the circle?

3) How far in a straight line (chord) is Person A from Person C?

4) The prayer circle is formed on a square lawn measuring 25x25 feet. What is the maximum number of people who could stand in the circle and still be 6 feet apart?

No 4

sinθ > 3/12.5

θ >13.8865

2θ > 27.773

Max people < 360/27.773

Max people < 12.962

Max people = 12

Again, I don't really understand what is "stand in the circle" .... I assumed stand along the circle circumference.

Quote:IAchance5Been a while, so hopefully I'm thinking on the right lines.....

Since the chord between 2 people is 6, then the radius of circle will be 7.89ft (6/(2 sin(.39 radians))

1) C = 49.57ft

2) d = 15.78ft

3) AC cord = 11.15ft (2*7.89) sin(.785 radians)

4) 12 people at most.....if we went to 13 people then we would go slightly over the radius of 12.5.....12.62 would be the radius for 13 people

1) Very close

2) Very close

3) Very close

4) Correct!

Quote:Wizard

radius = 3/sin(22.5) = 7.839377789

1. 2*pi*radius = 6*pi/sin(22.5) = 49.2563

2. 2*radius = 6/sin(22.5) = 15.6788

3. sqrt(2)*radius = 3*sqrt(2)/sin(22.5) = 11.0866

If this are right, I'll think about #4.

1) Correct!

2) Correct!

3) Correct!

Quote:ssho88No 4

sinθ > 3/12.5

θ >13.8865

2θ > 27.773

Max people < 360/27.773

Max people < 12.962

Max people = 12

Again, I don't really understand what is "stand in the circle" .... I assumed stand along the circle circumference.

4) Correct!

---------------------------------

<Insert your own prayer circle punchline here>

Call the worshipers A - M

With an odd number, there is nobody directly opposite A. Which means the people on the far side (#7=G & #8=H) are set in some from the opposite of the circle. i.e.

Assume the square is from y=+12.5 ft to -12.5 ft

Assume A is at the top border of the square (0,12.5)

With N=13, radius is r = 3/sin(.5*360/13) = 12.53574441 ft.

So center of circle would be at (0,-0.0357441)

The (horizontal) cord between the 7th person (G) and 8th person (H) is a distance of r * cos(.5*360/13) = 12.17147846 below the center of the circle at y=-12.20722256 ft. ...(from x = +3ft to -3ft for G & H respectively)

Thus G & H are still on the square lawn, even though the imaginary circle they are standing on (diameter = 2*12.5357441 = 25.07148882) extends out of the square.

If they hold hands along the cord (which seems likely), I think 13 fit entirely on the lawn.

If their arms curve along the circle, they are all standing on the lawn, but their arms would extend to an area above the boundary.....which I might argue the prayer "circle" is still standing in the square lawn.

Only if you need to paint the entire circle on the lawn so they know where to stand do you get limited to 12

14 still doesn't seem to work

***Waiting for the marbles to come out!***

(Except for the one in the lower left who is checking out that sexy b**ch next to him!)

Quote:Gialmere4) The prayer circle is formed on a square lawn measuring 25x25 feet. What is the maximum number of people who could stand in the circle and still be 6 feet apart?

I'm also confused by what is being asked of #4. Must the worshippers stand on the circumference of a circle? May they stand inside of it? Why mention a square, can't you just say the diameter of the circle is 25 feet?

Quote:WizardYou put $1 in a bank account at a fixed interest rate of 10%, compounded monthly. Over an infinite period of time, what ratio of the time will the balance start with a 1?