Question

În trapezul ABCD, AB||CD, AB=15 cm, CD=25 cm, AC=20 cm si BD=24 cm. Daca AC^BD={O}, calcultati AO, OC, BO si OD. Dau COROANA !

Answer 1

AB||CD⇒ΔAOB~ΔCOD⇒[tex] \frac{AB}{DC}= \frac{AO}{OC}= \frac{OB}{OD} [/tex]⇒$\frac{AB+DC}{DC}= \frac{AO+OC}{OC}= \frac{BO+OD}{OD}$
Dar noi stim ca AO+OC=AC=20cm
               iar BO+OD=BD=24 cm
Atunci vom avea:
$\frac{40}{25}= \frac{20}{OC}= \frac{24}{OD}$
Deci vom avea:
$OC= \frac{25*20}{40}= \frac{25}{2}=12,5 cm$
$OD= \frac{25*24}{40}=15 cm$
OA=AC-OC
OA=20-12,5⇒OA=7,5 cm
OB=BD-OD
OB=24-15⇒OB=9cm