## BdMO National Higher Secondary 2010/4

BdMO
Posts: 134
Joined: Tue Jan 18, 2011 1:31 pm

### BdMO National Higher Secondary 2010/4

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\$.

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

### Re: BdMO National Higher Secondary 2010/4

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?

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

### Re: BdMO National Higher Secondary 2010/4

I have found a solution here.