USA TST 2007
- FahimFerdous
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Triangle $ABC$ is inscribed in circle $W$. The tangent lines to $W$ at $B$ and $C$ meet at $T$. Point $S$ lies on ray $BC$ such that $AS$ is perpendicular to $AT$. points $B_1$ and $C_1$ lies on ray $ST$ (with $C_1$ in between $B_1$ and $S$) such that $B_1T$=$BT$=$C_1T$. Prove that triangles $ABC$ and $AB_1C_1$ is similar.
Last edited by FahimFerdous on Sun Apr 15, 2012 1:25 pm, edited 1 time in total.
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Re: USA TST 2007
Shouldn't that be $C_1T$? Please clarify.FahimFerdous wrote: such that $B_1T$=$BT$=$CT_1$.
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- FahimFerdous
- Posts:176
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Re: USA TST 2007
Hint:
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- Phlembac Adib Hasan
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Re: USA TST 2007
Here is my proof.Please somebody check it if there is any mistake.(As it is in my nature)
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Re: USA TST 2007
It seems quite okay to me, but you should try reading http://yufeizhao.com/olympiad/cyclic_quad.pdf
You can use the lemmas found there to prove it much easily.
You can use the lemmas found there to prove it much easily.
Please read Forum Guide and Rules before you post.
Use $L^AT_EX$, It makes our work a lot easier!
Nur Muhammad Shafiullah | Mahi
Use $L^AT_EX$, It makes our work a lot easier!
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Re: USA TST 2007
$\text{Another solution}$:
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