Twierdzenia

Spis twierdzeń:

(1)
\begin{align} {a \over \sin \alpha}={b \over \sin \beta}={c \over \sin \gamma}=2R \end{align}
(2)
\begin{align} \left\{\begin{array}{l l} a^2=b^2+c^2-2bc\cos\alpha\\ b^2=c^2+a^2-2ca\cos\beta\\ c^2=a^2+b^2-2ab\cos\gamma \end{array} \right. \end{align}
(3)
\begin{equation} u^2a =b^2 x+c^2 y-axy \end{equation}
(4)
\begin{align} \frac{BX}{XC}\cdot\frac{CY}{YA}\cdot\frac{AZ}{ZB}=1\Leftrightarrow \exists_O: O\in AX\wedge O\in BY\wedge O\in CZ \end{align}
(5)
\begin{align} \frac{\sin\sphericalangle BAX}{\sin\sphericalangle XAC}\cdot\frac{\sin\sphericalangle CBY}{\sin\sphericalangle YBA}\cdot\frac{\sin\sphericalangle AZC}{\sin\sphericalangle ZCB}=1\Leftrightarrow \exists_O: O\in AX\wedge O\in BY\wedge O\in CZ \end{align}
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