ganeshie8
  • ganeshie8
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
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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ganeshie8
  • ganeshie8
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 :)
Loser66
  • Loser66
why not??
Loser66
  • Loser66
\(\angle BAD =\angle CAD\) since arc BD = arc CD

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Loser66
  • Loser66
hence AD bisects BAD
ganeshie8
  • ganeshie8
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
ganeshie8
  • ganeshie8
Ahh wait I see what you're doing, you're saying "equal chords of the same circle intercept equal angles" ?
Loser66
  • Loser66
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.
ganeshie8
  • ganeshie8
That should do! thanks!
Loser66
  • Loser66
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
ganeshie8
  • ganeshie8
It is already there but hidden... just scroll down on the left hand side, do you see "Conic" section ?
ganeshie8
  • ganeshie8
|dw:1437918190532:dw|
Loser66
  • Loser66
got it!! thanks a lot
Loser66
  • Loser66
I got it!! lalala...
Loser66
  • Loser66
Empty
  • Empty
Ahhhh I missed the conversation because someone deleted their comments
Loser66
  • Loser66
@Empty the conversation I deleted was irrelevant to the problem. :)
Empty
  • Empty
Haha that's fine, I say irrelevant stuff all the time :P I kinda like distractions
ganeshie8
  • ganeshie8
Thats really a clever way to prove both the things one shot : I is the incenter and lies on the circle
ganeshie8
  • ganeshie8
@Concentrationalizing
nincompoop
  • nincompoop
I like the third paragraph in this: http://mathworld.wolfram.com/Collinear.html

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