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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.