BdMO National Higher Secondary 2019/7

Discussion on Bangladesh Mathematical Olympiad (BdMO) National
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samiul_samin
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BdMO National Higher Secondary 2019/7

Unread post by samiul_samin » Mon Mar 04, 2019 9:40 am

Given three cocentric circles $\omega_1$,$\omega_2$,$\omega_3$ with radius $r_1,r_2,r_3$ such that $r_1+r_3\geq {2r_2}$.Constrat a line that intersects $\omega_1$,$\omega_2$,$\omega_3$ at $A,B,C$ respectively such that $AB=BC$.

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samiul_samin
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Re: BdMO National Higher Secondary 2019/7

Unread post by samiul_samin » Thu Mar 14, 2019 11:01 am

Diagram
2019-03-14 08.51.48-1-3.png
2019-03-14 08.51.48-1-3.png (22.76 KiB) Viewed 660 times
This diagram is for \[r_1+r_3=2r_2\]

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math_hunter
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Re: BdMO National Higher Secondary 2019/7

Unread post by math_hunter » Fri Mar 15, 2019 7:47 pm

Have you got the solution of this problem???

soyeb pervez jim
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Re: BdMO National Higher Secondary 2019/7

Unread post by soyeb pervez jim » Sat Mar 16, 2019 12:51 am

May be not for all cases $AB=BC$ can't be drawn even if $r_1+r_3\geq 2r_2$. I think $2r_{2}^{2} \geq r_{1}^{2}+r_{3}^{2}$ also must hold

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