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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
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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ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1Exactly, 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
 one year ago
Best ResponseYou've already chosen the best response.2\(\angle BAD =\angle CAD\) since arc BD = arc CD

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1I 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
 one year ago
Best ResponseYou've already chosen the best response.1Ahh wait I see what you're doing, you're saying "equal chords of the same circle intercept equal angles" ?

Loser66
 one year ago
Best ResponseYou've already chosen the best response.2I 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
 one year ago
Best ResponseYou've already chosen the best response.1That should do! thanks!

Loser66
 one year ago
Best ResponseYou've already chosen the best response.2However, 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
 one year ago
Best ResponseYou've already chosen the best response.1It is already there but hidden... just scroll down on the left hand side, do you see "Conic" section ?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1dw:1437918190532:dw

Empty
 one year ago
Best ResponseYou've already chosen the best response.0Ahhhh I missed the conversation because someone deleted their comments

Loser66
 one year ago
Best ResponseYou've already chosen the best response.2@Empty the conversation I deleted was irrelevant to the problem. :)

Empty
 one year ago
Best ResponseYou've already chosen the best response.0Haha that's fine, I say irrelevant stuff all the time :P I kinda like distractions

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1Thats really a clever way to prove both the things one shot : I is the incenter and lies on the circle

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1@Concentrationalizing

nincompoop
 one year ago
Best ResponseYou've already chosen the best response.0I like the third paragraph in this: http://mathworld.wolfram.com/Collinear.html
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