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Math Help - The alternate segment theorem

  1. #1
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    The alternate segment theorem

    this is a well above the standed question for a yr 10 geometry assignment i am working on


    so the first thing i did was to draw a diameter from a to a new point g, which the i joined two lines from g to d and e, the next thing i did was to find 3 right angles in the circle so i could try to find a relationship between g,d,a and a,e,d


    but now i am kinda stuck

    any help would be greatly appreciated

    thanks

    Zac
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  2. #2
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    Quote Originally Posted by zp3929 View Post
    this is a well above the standed question for a yr 10 geometry assignment i am working on


    ...
    Zac
    I've modified your drawing a little bit.

    1. Draw a perpendicular bisector of AD.

    2. |\xi| = |\epsilon|

    3. \angle(MAB) = 90^\circ because the radius is perpendicular to the tangent in the tangent point.

    4. |\alpha| = 90^\circ - |\xi| = 90^\circ - |\epsilon|

    5. |\tau| = 90^\circ - |\alpha| = 90^\circ - (90^\circ - |\epsilon|) ~\implies~ \boxed{|\tau| = |\epsilon|}
    Attached Thumbnails Attached Thumbnails The alternate segment theorem-sehnen_tangentwinkel.gif  
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  3. #3
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    Quote Originally Posted by zp3929 View Post
    this is a well above the standed question for a yr 10 geometry assignment i am working on


    so the first thing i did was to draw a diameter from a to a new point g, which the i joined two lines from g to d and e, the next thing i did was to find 3 right angles in the circle so i could try to find a relationship between g,d,a and a,e,d


    but now i am kinda stuck

    any help would be greatly appreciated

    thanks

    Zac
    Read this: VICIOUS CIRLES: The Alternate Segment Theorem!

    Or this: Circle Theorems

    Or even this: http://www.benjamin-mills.com/maths/...rems-proof.pdf (not bad for a student of his age)
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