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Math Help - Proving a triangle in a circle is degenerate

  1. #1
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    Proving a triangle in a circle is degenerate

    How do I prove that a triangle inscribed in a circle (where all 3 sides are touching the circumference of the circle) is degenerate when above 135 degrees?

    Just a part of a problem im working on and im nearly there but i need to prove this part
    Cheers
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  2. #2
    Senior Member abhishekkgp's Avatar
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    Re: Proving a triangle in a circle is degenerate

    Quote Originally Posted by pikachu26134 View Post
    How do I prove that a triangle inscribed in a circle (where all 3 sides are touching the circumference of the circle) is degenerate when above 135 degrees?

    Just a part of a problem im working on and im nearly there but i need to prove this part
    Cheers
    No this is not true. You have posted a problem where the things are different, i was not trying to say that any triangle having one of its angles as 135 deg is degenerate. You can circumscribe any triangle by a circle. A 135,22.5,22.5 triangle is of course non degenerate. Circumscribing it wouldn't make it degenerate!!!
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  3. #3
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    Re: Proving a triangle in a circle is degenerate

    Hello, pikachu26134!

    Perhaps if you give us the original problem,
    . . your question will make sense.


    How do I prove that a triangle inscribed in a circle
    (where all 3 sides are touching the circumference of the circle)
    is degenerate when above 135 degrees?

    You say that the triangle is inscribed in a circle.
    . . (The triangle is inside the circle; the vertices touch the circle.)

    Yet you say the sides are touching the circle.
    . . Perhaps you mean "a circle is inscribed in a triangle"?

    Also, what is above 135 degrees?


    You begin with "We have a triangle."
    Then add that it has either an incircle or a circumcircle.
    Then (I think) make one angle greater than 135 degrees.
    And now we don't have a triangle ?
    . . (It shrinks to a point?)

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