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BdMO National Higher Secondary 2019/7

Posted: Mon Mar 04, 2019 9:40 am
by samiul_samin
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 $AB=BC$.

Re: BdMO National Higher Secondary 2019/7

Posted: Thu Mar 14, 2019 11:01 am
by samiul_samin
Diagram
2019-03-14 08.51.48-1-3.png
This diagram is for \[r_1+r_3=2r_2\]

Re: BdMO National Higher Secondary 2019/7

Posted: Fri Mar 15, 2019 7:47 pm
by math_hunter
Have you got the solution of this problem???

Re: BdMO National Higher Secondary 2019/7

Posted: Sat Mar 16, 2019 12:51 am
by soyeb pervez jim
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

Re: BdMO National Higher Secondary 2019/7

Posted: Sat Feb 06, 2021 9:07 pm
by Anindya Biswas
This problem is just asking for a triangle whose $2$ sides and median on the third side is given.

Re: BdMO National Higher Secondary 2019/7

Posted: Sun Feb 07, 2021 1:06 am
by Anindya Biswas
samiul_samin wrote:
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 $AB=BC$.
Draw a parallelogram with side lengths $r_1$ and $r_3$ and with a diagonal of length $2r_2$. The other diagonal of this parallelogram is the required segment.

Re: BdMO National Higher Secondary 2019/7

Posted: Sun Feb 28, 2021 2:21 pm
by hriditapaul
Can you show the proof?

Re: BdMO National Higher Secondary 2019/7

Posted: Mon Mar 01, 2021 1:13 pm
by Anindya Biswas
hriditapaul wrote:
Sun Feb 28, 2021 2:21 pm
Can you show the proof?
Diagonals of parallelogram bisects each other.