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ganeshie8

  • one year ago

Let Γ be the circumcircle of ΔABC and let D be the midpoint of the arc BC. Prove that below three points are collinear : 1) A 2) the incenter I of ΔABC 3) D http://tube.geogebra.org/m/1437801

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  1. ganeshie8
    • one year ago
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    Exactly, but somehow I find below statement not so obvious "D lies on the angle bisector of angle A" just looking for a proof if it is easy :)

  2. Loser66
    • one year ago
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    why not??

  3. Loser66
    • one year ago
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    \(\angle BAD =\angle CAD\) since arc BD = arc CD

  4. Loser66
    • one year ago
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    hence AD bisects BAD

  5. ganeshie8
    • one year ago
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    I can't answer "why not" because idk lol By definition, \(I\) lies on the angel bisector... but not so much about the point \(D\) is known right

  6. ganeshie8
    • one year ago
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    Ahh wait I see what you're doing, you're saying "equal chords of the same circle intercept equal angles" ?

  7. Loser66
    • one year ago
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    I don't know the name of the property but it is!! if the arcs of the angles are equal, then the angles are equal.

  8. ganeshie8
    • one year ago
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    That should do! thanks!

  9. Loser66
    • one year ago
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    However, the original problem is not a piece of cake. I didn't find out the logic yet!! ha!! Can you please help me draw out the circle center D that goes through B? I need it to prove O is the incenter of \(\triangle ABC\). Please

  10. ganeshie8
    • one year ago
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    It is already there but hidden... just scroll down on the left hand side, do you see "Conic" section ?

  11. ganeshie8
    • one year ago
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    |dw:1437918190532:dw|

  12. Loser66
    • one year ago
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    got it!! thanks a lot

  13. Loser66
    • one year ago
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    I got it!! lalala...

  14. Loser66
    • one year ago
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  15. Empty
    • one year ago
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    Ahhhh I missed the conversation because someone deleted their comments

  16. Loser66
    • one year ago
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    @Empty the conversation I deleted was irrelevant to the problem. :)

  17. Empty
    • one year ago
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    Haha that's fine, I say irrelevant stuff all the time :P I kinda like distractions

  18. ganeshie8
    • one year ago
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    Thats really a clever way to prove both the things one shot : I is the incenter and lies on the circle

  19. ganeshie8
    • one year ago
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    @Concentrationalizing

  20. nincompoop
    • one year ago
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    I like the third paragraph in this: http://mathworld.wolfram.com/Collinear.html

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