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Math Help - [SOLVED] Finding diameter of a cone

  1. #1
    Blain
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    [SOLVED] Finding diameter of a cone

    I have a sphere at origin and a known 3d point outside the sphere.
    How do I calc the diameter of the cone created by the 3d point
    and it's intersection with the sphere (if that makes sense)

    Thanks
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  2. #2
    Super Member
    earboth's Avatar
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    Quote Originally Posted by Blain
    I have a sphere at origin and a known 3d point outside the sphere.
    How do I calc the diameter of the cone created by the 3d point
    and it's intersection with the sphere (if that makes sense)

    Thanks
    Hello,

    I've attached a diagram to show you what I've calculated.

    All lines PT form a cone. C is the centre of the sphere. All triangles CTP are right triangles. So the diametre of the cone's base is 2 times the height in the right triangle. The height in a right triangle (and only there) can be calculated by:
    h={{r \cdot TP}\over CP}

    If you know the length of the three lines you only have to plug in the values and caculate the radius of the base.

    Greetings

    EB
    Attached Thumbnails Attached Thumbnails [SOLVED] Finding diameter of a cone-beruehrkegel.gif  
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  3. #3
    Super Member
    earboth's Avatar
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    Quote Originally Posted by Blain
    I have a sphere at origin and a known 3d point outside the sphere.
    How do I calc the diameter of the cone created by the 3d point
    and it's intersection with the sphere (if that makes sense)

    Thanks
    Hello,

    it's me again:
    I've attached a picture which shows sphere and cone from outer space. May be this will help to understand my previous diagram.

    Greetings

    EB
    Attached Thumbnails Attached Thumbnails [SOLVED] Finding diameter of a cone-beruehrkegl2.gif  
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