证明:CD=AC*CB÷根号下(AC^+BC^) CD^=AC^BC^/AC^+BC^ 1/AC^+1/BC^=AC^+BC^/AC^BC^=1/CD^.
AC方=AD*AB,BC方=BD*AB,CD方=AD*BD(射影定理,可用相似证明)1/AC方+1/BC方=(AD+BD)/(AD*BD*AB)=AB/(CD方*AB)=/CD方