**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 $x$.