BdMO National Higher Secondary 2010/4

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BdMO
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BdMO National Higher Secondary 2010/4

Unread post by BdMO » Mon Feb 07, 2011 12:08 am

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 $x$.

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samiul_samin
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Re: BdMO National Higher Secondary 2010/4

Unread post by samiul_samin » Mon Feb 25, 2019 3:40 pm

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?

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samiul_samin
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Re: BdMO National Higher Secondary 2010/4

Unread post by samiul_samin » Sun Mar 10, 2019 10:21 pm

I have found a solution here.

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