This is called as Pancake Theorem.I think that this theorem is wonderful. Let $C$ be circle of which all points are inside $r$ be radius of $C$ $X$ be arbitrary fixed point on the circumference $P$ be moving point on the circumference $x$ be distance from $X$ to $P$ on the circumference $l(P)$ be diameter which pass $P$ $r(P)$ be median line of $M_{1}$ which is perpendicular to $l(P)$ $b(P)$ be median line of $M_{2}$ which is perpendicular to $l(P)$ $f_r(x)$ be distance from $P$ to $r(P)$ $f_b(x)$ be distance from $P$ to $b(P)$ Let $x$ move from $0$ to $\pi r$.Then $f_r(x)-f_b(x)$ moves from $f_r(0)-f_b(0)$ to $f_r(\pi r)-f_b(\pi r)=(2r-f_r(0))-(2r-f_b(0))=-(f_r(0)-f_b(0))$.Obviously $f$ is continuous.Thus ∃$x_0(0\le x_0\le \pi r)$ s.t. $f_r(x_0)-f_b(x_0)=0$ by intermediate value theorem.Therefore the proof is completed.$\blacksquare$