Răspuns:
a) BD = 6cm, DC = 4cm; b) P(ABDE) = 22,2cm
Explicație pas cu pas:
teorema bisectoarei:
[tex]\frac{AB}{BD} =\frac{AC}{DC} \iff \frac{9}{BD} =\frac{6}{DC}\\9DC = 6BD\\BD + DC = BC \implies BD = 10 - DC\\9DC = 6(10 - DC)\\15DC = 60 \implies \bf DC = 4\ \ cm\\BD = 10 - 4 = 6 \implies \bf BD = 6\ \ cm[/tex]
ΔEDC ~ ΔABC
[tex]\frac{ED}{AB} = \frac{EC}{AC} = \frac{DC}{BD}\\\frac{ED}{9} = \frac{EC}{6} = \frac{4}{10} = \frac{2}{5}\\DE = \frac{18}{5} \implies DE = 3,6cm\\EC = \frac{12}{5} \implies EC = 2,4cm\\AE = AC - EC = 6 - 2,4 = 3,6 cm[/tex]
Perimetrul (ABDE) = AB + BD + DE + AE = 9 + 6 + 3,6 + 3,6 = 22,2 cm
