2012 China TST Quiz1-Day1-p2
Posted: Fri Mar 23, 2012 10:52 am
$ABC$ is a scalene triangle ,the incircle touches $BC,CA,AB$ at $A_1,B_1,C_1$ respectively.
$A_2$ is the symmetric point of $A_1$ about $B_1C_1$.$B_2,C_2$ are defined similarly.
$AA_2 \cap BC=A_3$,$B_3,C_3$ are defined similarly.Prove that $A_3,B_3,C_3$ are collinear.
[Hint:Straightforward complex yields they lie on euler line of $\triangle ABC$.So it should work with euclid too.i'm not sure but maybe Menelaus is more useful than angle chasing here.
]
$A_2$ is the symmetric point of $A_1$ about $B_1C_1$.$B_2,C_2$ are defined similarly.
$AA_2 \cap BC=A_3$,$B_3,C_3$ are defined similarly.Prove that $A_3,B_3,C_3$ are collinear.
[Hint:Straightforward complex yields they lie on euler line of $\triangle ABC$.So it should work with euclid too.i'm not sure but maybe Menelaus is more useful than angle chasing here.
]