Question

triunghiul dreptunghic ABC,cu BAC=90 grade si C=30.bisectoarea BD a unghiului ABC intersecteaza latura AC in punctul D,iar AD=4cm.lungimea laturii AC este:

a)6 cm

b)8 cm

c)12cm

d)16cm​

Answer 1

$\it Th.\ \angle 30^o \Rightarrow BC=2AB\ \ \ \ \ (1)\\ \\ Th.\ bisectoarei \Rightarrow \dfrac{AD}{DC}=\dfrac{AB}{BC}\ \stackrel{(1)}{\Longrightarrow}\ \dfrac{4}{DC}=\dfrac{AB}{2AB} \Rightarrow \dfrac{4}{DC}=\dfrac{1}{2} \Rightarrow DC=8\ cm\\ \\ AC=AD+DC=4+8=12\ cm$