Question

In trapezul ABCD AB//CD AB=15 cm CD=21 cm AC=18 cm si BD=24 cm Daca AC reunit cu BD in punctul O calculati, AO OC BO si OD.

Answer 1

CF/BC=OF/AB ⇒(BC-BF)/BC=OF/15
⇒BC/BC-BF/BC=OF/15 ⇒ 1- BF/BC=OF/15 (1)
BF/BC=OF/DC ⇒BF/BC=OF/25 (2)


(1)+(2)⇒
1-BF/BC+BF/BC=OF/15 +OF/25
1=OF/15 +OF/25 = 5*OF/75+ 3*OF/75 =8*OF/75
⇒ OF=75/8


BO/BD=OF/DC
BO/24=75/(8*25)=3/8
BO=24*3/8=3*3
BO=9
⇒OD=BD-BO=24-9
OD=15


BO/BD=AO/AC ⇒ 9/24=AO/20 ⇒
AO=20*9/24=5*9/6 =15/2
AO=7,5
OC=AC-AO=20-15/2=40/2-15/2=25/2
OC=12.5