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Math Help - Exterior circle angles, how to calculate?

  1. #1
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    Exterior circle angles, how to calculate?

    I'm trying to ascertain some angles from a 'circle within a square'. Where the circle intersects the square at four points, and then separates, as a quadrant, then a quarter way round intersects the square again. I'd like to be able to work out the angle at some points along the circle edge in relationship to the square...
    So to simplify it... I've drawn it! See attachment.
    There are two angle concepts, the red one from the point of intersection of circle and square, and the blue one which is a subsequent angle, having ascertained two of the red angle...I guess.
    Any help with this would be much appreciated.
    Attached Thumbnails Attached Thumbnails Exterior circle angles, how to calculate?-circles-2.jpg  
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  2. #2
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    Re: Exterior circle angles, how to calculate?

    Quote Originally Posted by Rhoops View Post
    I'm trying to ascertain some angles from a 'circle within a square'. Where the circle intersects the square at four points, and then separates, as a quadrant, then a quarter way round intersects the square again. I'd like to be able to work out the angle at some points along the circle edge in relationship to the square...
    So to simplify it... I've drawn it! See attachment.
    There are two angle concepts, the red one from the point of intersection of circle and square, and the blue one which is a subsequent angle, having ascertained two of the red angle...I guess.
    Any help with this would be much appreciated.
    1. Draw the radii from A and D to the midpoint of the circle.

    2. Then have a look here: Inscribed angle - Wikipedia, the free encyclopedia

    and here: Tangent lines to circles - Wikipedia, the free encyclopedia
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  3. #3
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    Re: Exterior circle angles, how to calculate?

    Hi Rhoops,
    To your drawing show O center of circle,OA,OD.CD extended meeting diameter 2AB at K. Assume AC =50 then OK =50.Angle ODK has a sine value of 50/100 so it is 30 deg. AOD =30 deg the central angle of arc AD. Angle CAD = 1/2 AOD =15 deg, The two angles at D are 15 deg. Follow the same procedure to find other CAD angles


    bjh
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    Re: Exterior circle angles, how to calculate?

    Thank you both for the help. All sorted! I'm looking for a change in angle at a specific point in the early stages of AB that needs to be about 0.45 degrees, and that seems to fit quite nicely!! Much obliged.
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