Steiner’s theorem

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

$$\frac{BM}{MC}\cdot \frac{BN}{NC}=\frac{A{B}^2}{A{C}^2}$$

Title	Steiner’s theorem
Canonical name	SteinersTheorem
Date of creation	2013-03-22 13:21:41
Last modified on	2013-03-22 13:21:41
Owner	mathcam (2727)
Last modified by	mathcam (2727)
Numerical id	6
Author	mathcam (2727)
Entry type	Theorem
Classification	msc 51N20