Question

formula razei cercului va rog

Answer 1

Raza cercului circumscris in triunghi: 

$\frac{a}{sinA}= \frac{b}{sinB}= \frac{c}{sinC}=2R & \ \Leftrightarrow & \ \frac{BC}{sinA}= \frac{AC}{sinB}= \frac{AB}{sinC}=2R$

$R = \frac{a\cdot b\cdot c}{4\cdot S_{\Delta ABC} } & \ \Leftrightarrow & \ R = \frac{BC\cdot AC\cdot AB}{4\cdot S_{\Delta ABC} }$

Raza cercului inscris in triunghi:

$r = \frac{S_{\Delta ABC }}{P_{\Delta ABC}}$

$r = 4R\cdot sin \frac{\hat A}{2} \cdot sin \frac{\hat B}{2} \cdot sin \frac{\hat C}{2}$