Question

Calcule x e y nos triângulos acd abaixo, sabendo que a é bissetriz interna do ângulo A

Answer 1

$\displaystyle \sf x+y = 12 \\\\ y = 12-x\\\\ \underline{ \text{Teorema da bissetriz interna}} : \\\\ \frac{AC}{NC}=\frac{AD}{ND} \\\\\\ \frac{5}{x}=\frac{10}{y} \\\\\\ \frac{1}{x}=\frac{2}{y} \\\\\\ y =2x \\\\ 12-x=2x \\\\ 12 = x+2x \\\\ 3x = 12 \to \boxed{\sf x = 4 }\\\\ y = 12-4 \to\boxed{\sf y = 8}$