Question

mate clasa a 7a


ABCD trapez
AB || CD
AB > CD
AC intersectat cu BD={O}
OD/OB=3/5
AC=48 cm

OC=?
OA=?

desenul l am facut, dar nu inteleg problema =))

Answer 1

Răspuns:

$AB\parallel CD$

Din teorema lui Thales avem $\frac{OD}{OB}=\frac{OC}{OA}$

$\frac{OC}{OA}=\frac{3}{5} \\ \\ \frac{OC}{AC}=\frac{OC}{OA+OC}=\frac{3}{5+3}=\frac{3}{8} \\ \\ OC=\frac{3}{8}\times AC=\frac{3}{8}\times 48=18~cm \\ \\ OA=48-18=30~cm$