## BdMO National Higher Secondary 2019/7

Discussion on Bangladesh Mathematical Olympiad (BdMO) National
samiul_samin
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Joined: Sat Dec 09, 2017 1:32 pm

### BdMO National Higher Secondary 2019/7

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 $AB=BC$.

samiul_samin
Posts: 1007
Joined: Sat Dec 09, 2017 1:32 pm

### Re: BdMO National Higher Secondary 2019/7

Diagram
2019-03-14 08.51.48-1-3.png (22.76 KiB) Viewed 7176 times
This diagram is for $r_1+r_3=2r_2$

math_hunter
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Joined: Mon Sep 24, 2018 10:33 pm
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### Re: BdMO National Higher Secondary 2019/7

Have you got the solution of this problem???

soyeb pervez jim
Posts: 21
Joined: Sat Jan 28, 2017 11:06 pm

### Re: BdMO National Higher Secondary 2019/7

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