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Geometry help

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  • 23-11-2014 11:13am
    #1
    fjon
    Registered Users Posts: 2,084 ✭✭✭


    I'm doing a geocaching puzzle that requires me to solve a sangaku and I'm a bit rusty on my maths.

    The puzzle is here, and the given information is the radius of the purple circle 乙 is 3.06. I need to get the radius of the red circle.

    Could someone give me some pointers as to how to being this? I don't necessarily want someone to just solve it, but would like to do it myself. Bear in mind it's nearly 20 years since I did anything like this in my Leaving Cert.

    Thanks in advance!


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    #2
    Ciaran
    Registered Users Posts: 908 ✭✭✭Ciaran


    fjon wrote: »
    I'm doing a geocaching puzzle that requires me to solve a sangaku and I'm a bit rusty on my maths.

    The puzzle is here, and the given information is the radius of the purple circle 乙 is 3.06. I need to get the radius of the red circle.

    Could someone give me some pointers as to how to being this? I don't necessarily want someone to just solve it, but would like to do it myself. Bear in mind it's nearly 20 years since I did anything like this in my Leaving Cert.

    Thanks in advance!
    Try to see how the length of the sides of the square, and the diameters of the orange, purple and red circles relate to each other.

    The diagonal line in the square, a horizontal line from the centre to the left of the purple circle and two lines from the centre of the red circle, one vertically down and one to the centre of the square should help.


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    #3
    fjon
    Registered Users Posts: 2,084 ✭✭✭fjon


    Ciaran wrote: »
    Try to see how the length of the sides of the square, and the diameters of the orange, purple and red circles relate to each other.

    The diagonal line in the square, a horizontal line from the centre to the left of the purple circle and two lines from the centre of the red circle, one vertically down and one to the centre of the square should help.

    Ok, thanks for that!
    This is what I have:
    Diagonal line in square = diameter of circle (I'll call it "c")
    The side of the square (call them "a" and "b") would then be got with a= sqrt[c^2 - b^2]
    I believe if I have the dimensions of the triangle I can get the radius of the incircle with:
    r=At/s, where r=radius, At= area of triangle, and s= semi-perimiter.

    However, I'm not sure how any of this helps me with the purple circle.

    Your notes for drawing lines - would you know if there is any tool online I can use to draw these? I don't have a compass so don't think I can do it on paper.


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    #4
    Ciaran
    Registered Users Posts: 908 ✭✭✭Ciaran


    fjon wrote: »
    Diagonal line in square = diameter of circle (I'll call it "c")
    The side of the square (call them "a" and "b") would then be got with a= sqrt[c^2 - b^2]
    It's a square so a=b. Then c = a*sqrt(2)
    I believe if I have the dimensions of the triangle I can get the radius of the incircle with:
    r=At/s, where r=radius, At= area of triangle, and s= semi-perimiter.
    That works. Get the area of the triangle and the semi perimeter in terms of the side length of the square and then you'll have the radius of the red circle in terms of the side length of the square.
    However, I'm not sure how any of this helps me with the purple circle.
    If you imagine a horizontal line from the left edge of the purple circle to the centre of the big circle. Its length is c from above (it's a radius of the big circle). It's also made up of the diameter of the purple circle and half the edge length of the square (a above). You should be able to work out the radius of the purple circle in terms of the side length of the square then. and you can compare it to the radius of the red circle.
    Your notes for drawing lines - would you know if there is any tool online I can use to draw these? I don't have a compass so don't think I can do it on paper.
    A rough freehand sketch would be sufficient to get the idea I think.


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    #5
    fjon
    Registered Users Posts: 2,084 ✭✭✭fjon


    That's great, I've drawn it out like you said and it did help me somewhat:

    Diameter of purple circle = 6.12
    c = diameter large circle
    a = side of square

    a = (c - 6.12)*2

    I can't get any further from there, and I feel like I may be overcomplicating something here.


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    #6
    Ciaran
    Registered Users Posts: 908 ✭✭✭Ciaran


    fjon wrote: »
    That's great, I've drawn it out like you said and it did help me somewhat:

    Diameter of purple circle = 6.12
    c = diameter large circle
    a = side of square

    a = (c - 6.12)*2

    I can't get any further from there, and I feel like I may be overcomplicating something here.
    From the diagonal of the square, you have that c = a*sqrt(2) so you can work out a and c from your equation there.


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