Results 1 to 6 of 6

Thread: Circles

  1. #1
    New Lounger
    Join Date
    Feb 2008
    Posts
    5
    Thanks
    0
    Thanked 0 Times in 0 Posts

    Circles

    The large circle has a diameter of 1m. The lines are at right angles.

    What is the diameter of the small circle?

    Tyler
    Attached Images Attached Images

  2. Subscribe to our Windows Secrets Newsletter - It's Free!

    Get our unique weekly Newsletter with tips and techniques, how to's and critical updates on Windows 7, Windows 8, Windows XP, Firefox, Internet Explorer, Google, etc. Join our 480,000 subscribers!

    Excel 2013: The Missing Manual

    + Get this BONUS — free!

    Get the most of Excel! Learn about new features, basics of creating a new spreadsheet and using the infamous Ribbon in the first chapter of Excel 2013: The Missing Manual - Subscribe and download Chapter 1 for free!

  3. #2
    Plutonium Lounger
    Join Date
    Mar 2002
    Posts
    84,353
    Thanks
    0
    Thanked 16 Times in 16 Posts

    Re: Circles

    <span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">3-2*SQRT(2) meters</span hide>

  4. #3
    New Lounger
    Join Date
    Feb 2008
    Posts
    5
    Thanks
    0
    Thanked 0 Times in 0 Posts

    Re: Circles

    Nice formula. I used pages of Pythagoras and came out at <span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">0.1768, 5mm more</span hide> .

    Tyler

  5. #4
    Plutonium Lounger
    Join Date
    Mar 2002
    Posts
    84,353
    Thanks
    0
    Thanked 16 Times in 16 Posts

    Re: Circles

    Here is the calculation:

    <span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">Let's call the radius of the large circle r and that of the small circle s
    BD = BC = r.
    Angle CAB is 45 degrees, so AB = BC/SQRT(2) = r/SQRT(2)
    PS = PC = s
    Angle CPQ is 45 degrees, so PQ = PC/SQRT(2) = s/SQRT(2)
    r = BD = AB + DA = AB + SQ = AB + SP + PQ = r/SQRT(2) + s + s/SQRT(2)
    Multiply both sides of the equation with SQRT(2):
    r*SQRT(2) = r + s*SQRT(2) + s
    s*(SQRT(2)+1) = r*(SQRT(2)-1)
    Multiply both sides with SQRT(2)-1:
    s*(SQRT(2)+1)*(SQRT(2)-1) = r*(SQRT(2)-1)*(SQRT(2)-1)
    s*(2-1) = r*(2-2*SQRT(2)+1)
    s = r*(3-2*SQRT(2)
    The diameter of the small circle is 2*s = 2*r*(3-2*SQRT(2)).
    Since r =1/2, s = 3-2*SQRT(2)</span hide>
    Attached Images Attached Images
    • File Type: png x.png (9.2 KB, 0 views)

  6. #5
    New Lounger
    Join Date
    Feb 2008
    Posts
    5
    Thanks
    0
    Thanked 0 Times in 0 Posts

    Re: Circles

    That’s neat.

    I did:

    A-G = SQRT((C-G*C-G)+(A-C*A-C))
    = 0.7071

    A-G+radius = 077071 + 0.5 = 1.2071

    A-F = 1.2071 – 1 = 0.2071

    A-E = 0.2071 * 0.7071 = 0.1464

    A-D = 0.2071 * 0.1464 = 0.03033

    D-F = (A-F) – (A-D) = 0.2071 – 0.03033 = 0.17677

    Answer = 176.8mm
    Attached Images Attached Images

  7. #6
    Plutonium Lounger
    Join Date
    Mar 2002
    Posts
    84,353
    Thanks
    0
    Thanked 16 Times in 16 Posts

    Re: Circles

    I can follow your calculation up to and including the line

    A-F = 1.2071 – 1 = 0.2071

    But I don't understand the next two lines:

    A-E = 0.2071 * 0.7071 = 0.1464

    A-D = 0.2071 * 0.1464 = 0.03033

Posting Permissions

  • You may not post new threads
  • You may not post replies
  • You may not post attachments
  • You may not edit your posts
  •