Tangentová věta

Technology
12 hours ago
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Albert Flores

Trojúhelník ABC V trigonometrii je tangentová věta tvrzení o rovinných trojúhelnících.

Pro každý trojúhelník ABC s vnitřními úhly α, β, γ a stranami a, b, c platí: :\frac{a-b}{a+b}=\frac{\mathrm{tg}\, \frac{\alpha -\beta }{2}}{\mathrm{tg}\, \frac{\alpha +\beta }{2}}={\mathrm{tg}\, \frac{\alpha -\beta }{2}}{\mathrm{tg}\, \frac{\gamma }{2}} :\frac{b-c}{b+c}=\frac{\mathrm{tg}\, \frac{\beta -\gamma }{2}}{\mathrm{tg}\, \frac{\beta +\gamma }{2}}={\mathrm{tg}\, \frac{\beta -\gamma }{2}}{\mathrm{tg}\, \frac{\alpha }{2}} :\frac{c-a}{c+a}=\frac{\mathrm{tg}\, \frac{\gamma -\alpha }{2}}{\mathrm{tg}\, \frac{\gamma +\alpha }{2}}={\mathrm{tg}\, \frac{\gamma -\alpha }{2}}{\mathrm{tg}\, \frac{\beta }{2}}

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