# Steiner’s theorem

Let $ABC$ be a triangle and $M,N\in(BC)$ be two points such that $m(\angle{BAM})=m(\angle{NAC})$. Then the cevians $AM$ and $AN$ are called isogonic cevians and the following relation holds:

 $\frac{BM}{MC}\cdot\frac{BN}{NC}=\frac{AB^{2}}{AC^{2}}$
Title Steiner’s theorem SteinersTheorem 2013-03-22 13:21:41 2013-03-22 13:21:41 mathcam (2727) mathcam (2727) 6 mathcam (2727) Theorem msc 51N20