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Thread: Circles

  1. #1
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    Circles

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

    What is the diameter of the small circle?

    Tyler
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  2. #2
    Plutonium Lounger
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    Re: Circles

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

  3. #3
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    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

  4. #4
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    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>
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  5. #5
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    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
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  6. #6
    Plutonium Lounger
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    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

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