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Math Help - Angles of a triangle with a tangent

  1. #1
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    Angles of a triangle with a tangent

    Just before any of you say anything; Yes, I posted this a few days ago, but I didn't do the diagram correctly so I'll just post this new thread.

    Okay, so :

    I'm trying to work out the angles on the triangle and I'm having a little bit of difficulty. I tried working it but I'm not getting anywhere. Would the angle at the right of the 65 be 25? And would the one opposite to the "25" be "90"?
    And by the way, the most important angle that I really need to get is the one at the tangent.
    Please, please, please help!

    Diagram :
    Attached Thumbnails Attached Thumbnails Angles of a triangle with a tangent-ocfpl.png  
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  2. #2
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    Re: Angles of a triangle with a tangent

    Quote Originally Posted by Kyleee View Post
    Just before any of you say anything; Yes, I posted this a few days ago, but I didn't do the diagram correctly so I'll just post this new thread.

    Okay, so :

    I'm trying to work out the angles on the triangle and I'm having a little bit of difficulty. I tried working it but I'm not getting anywhere. Would the angle at the right of the 65 be 25? And would the one opposite to the "25" be "90"?
    And by the way, the most important angle that I really need to get is the one at the tangent.
    Please, please, please help!

    Diagram :
    1. I've labeled the straight line segments and angles in your sketch. I assume that d is a diameter of the circle and that the upper left triangle is isosceles with x as equal legs (see attachment)

    2. If my assumptions are correct then

    • google for circle of Thales
    • \angle(A)=65^\circ Why?
    • \angle(A) + \angle(B) = 180^\circ Why?
    • \angle(D) + \angle(B) + \angle(C)= 180^\circ Why?
    • \angle(D) + \angle(E) = 90^\circ Why?
    Attached Thumbnails Attached Thumbnails Angles of a triangle with a tangent-winklimthaleskrs.png  
    Last edited by earboth; November 23rd 2011 at 01:35 AM.
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  3. #3
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    Re: Angles of a triangle with a tangent

    Hi Kyleee,
    You should state that the presumed diameter is perpendicular to the tangent at the point of tangency.
    The figure can be erected in an infinite number of ways unless the point on the circle at the 65 deg inscribed angle has a defined arc from the top or bottom of the circle.
    Wilmers assumption top arc= 90 deg
    Earboths assumption top arc =80deg
    bjh assumption top arc = 50 deg

    If you do not know how to calculate angles for these cases google
    chords and angles,complementry and supplemental angles, isosceles triangles
    Last edited by bjhopper; November 22nd 2011 at 07:31 PM. Reason: left out word
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