2.prove that this theorem holds if 1,2 or 3 of the points $P,Q,R$ lie on the extension.
3.prove that if $P,Q,R$ are collinear,$M$ lies on the circumcircle of $\triangle ABC$
[this theorem can be used in IMO-2011-6(i guess
)]Miquel's theorem-extensions-special cases
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Tahmid Hasan
- Posts:665
- Joined:Thu Dec 09, 2010 5:34 pm
- Location:Khulna,Bangladesh.
1.in $\triangle ABC$ let $P,Q,R$ be points on the interior $BC,CA,AB$ respectively.prove that the circumcircles of triangles $AQR,BPR,CPQ$ pass through a common point $M$.
2.prove that this theorem holds if 1,2 or 3 of the points $P,Q,R$ lie on the extension.
3.prove that if $P,Q,R$ are collinear,$M$ lies on the circumcircle of $\triangle ABC$
[this theorem can be used in IMO-2011-6(i guess )]
2.prove that this theorem holds if 1,2 or 3 of the points $P,Q,R$ lie on the extension.
3.prove that if $P,Q,R$ are collinear,$M$ lies on the circumcircle of $\triangle ABC$
[this theorem can be used in IMO-2011-6(i guess
)]বড় ভালবাসি তোমায়,মা