Question

In trapezul ABCD,AC se intersect.cu BD in punctul O.Daca AC=20cm si DO supra OB=3 supra 7, calculati lungimile segmentelor AO si CO. cum se rezolva?

Answer 1

nu e foarte greu, ducem diagonalele in trapez, avem AC=20 cm si:
DC || AB=> ΔOCD~ΔOAB <=> $\frac{OA}{OC}$ = $\frac{OD}{OB}$ = $\frac{DC}{AB}$ = $\frac{3}{7}$ <=> $\frac{0A}{OC}$ = $\frac{3}{7}$ => OA= $\frac{3}{7}$ * OC ,dar avem OA+OC=AC <=> $\frac{3}{7}$ * OC + OC=20 => OC= $\frac{7}{10}$ * 20 = 14 cm
OA= 20-14= 6 cm