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Math Help - Thales Theorem

  1. #1
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    Thales Theorem

    Prove the following.

    If the vertices of triangle ABC lie on a circle and AB is a diameter of that circle, then angle ACB is a right angle.

    I think that I need to use the Isosceles Triangle Theorem and the Angle Sum of a Triangle Theorem
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by MATNTRNG View Post
    Prove the following.

    If the vertices of triangle ABC lie on a circle and AB is a diameter of that circle, then angle ACB is a right angle.

    I think that I need to use the Isosceles Triangle Theorem and the Angle Sum of a Triangle Theorem
    See diagram
    Attached Thumbnails Attached Thumbnails Thales Theorem-gash.png  
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  3. #3
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    Thales theorem is a special case of the inscribed angle theorem which states that an angle inscribed in a circle is half of the central angle that subtends the same arc on the circle. Therefore, the angle does not change as its apex is moved to different positions on the circle.

    If angle inscribed in a circle and the central angle both subtend the semicircle then the central angle equals 180 and the angle inscribed equals half the central angle or 90.
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