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BdMO National Higher Secondary 2010/4

Posted: Mon Feb 07, 2011 12:08 am
by BdMO
Problem 4:
Given a point $P$ inside a circle $\Gamma$, two perpendicular chords through $P$ divide $\Gamma$ into distinct regions $a,\ b,\ c,\ d$ clockwise such that $a$ contains the centre of $\Gamma$.
Prove that \[ [a] + [c] \ge [ b ] + [d] \] Where $[x]$ = area of $x$.

Re: BdMO National Higher Secondary 2010/4

Posted: Mon Feb 25, 2019 3:40 pm
by samiul_samin
This problem is very easy to understand but I am not getting any way of solving the problem.Can anyone give me a hint at least or provide the proof?

Re: BdMO National Higher Secondary 2010/4

Posted: Sun Mar 10, 2019 10:21 pm
by samiul_samin
I have found a solution here.