Question

Considere o triangulo retangulo ABC da figura. Então, a medida do ralo da circunferencia inscrita no triangulo, sendo AB-5 cm, AC-12 cm e BC-13 cm. será B EL- >c А A) Tom O B) 2cm Ос) Зcm O D) 4cm O E) 5cm​

Answer 1

Vamos usar áreas.

$\displaystyle \sf \underline{\text{{\'A}rea do\ }\Delta_{ABC} }: \\\\ S_{ABC}=\frac{AC\cdot AB}{2} \\\\\\ S_{ABC}=\frac{12\cdot 5}{2} \\\\ S_{ABC}=30 \\\\\\ \underline{\text{{\'A}rea do\ }\Delta_{ABC} \ usando \ o\ circulo\ inscrito }: \\\\ S_{ABC}=p\cdot r \\\\ onde : \\\\\ p = \left(\frac{AB+AC+BC}{2} \right) \\\\ r = raio$

Daí, vamos substituir os respectivos valores na fórmula :

$\displaystyle \sf S_{ABC}=p\cdot r \\\\ 30=\left(\frac{AB+BC+AC}{2}\right)\cdot r \\\\\\ 30 = \left(\frac{12+5+13}{2}\right)\cdot r \\\\\\ 30 = 15\cdot r \\\\\ r = \frac{30}{15} \\\\\\ Potanto : \\\\ \huge\boxed{\sf r = 2 \ cm }$

letra b