Schooten定理是平面几何学最著名的定理之一,它的证明方法很多,本文介绍其中的十一种。 Schooten定理△ABC中,AD为∠BAC的平分线,D在BC上,则 AD~2=AB·AC-BD·DC。一、平几法证明证一利用辅助圆,相似法。过A、B、C三点作辅助圆,延长AD交圆于点E,连结BE(或CE)。由∠BAE=∠DAC,∠E=∠C,得△ABE∽ADC。 AB/AD=AE/AC。于是,AB·AC=AD·AE=AD(AD+ Schooten’s theorem is one of the most famous theorem of plane geometry. There are many methods for its verification. This paper introduces eleven of them. In Schooten’s theorem △ABC, AD is the bisector of BAC, and D is on BC, then AD~2=AB·AC-BD·DC. First, a few methods to prove that the first use of a test circle, similar to the law. Three points A, B and C are used as auxiliary circles, and AD is extended to point E to connect BE (or CE). By ∠ BAE = ∠ DAC, ∠ E = ∠ C, get △ ABE ∽ ADC. AB/AD=AE/AC. So, AB·AC=AD·AE=AD(AD+