Question

In the given figure shown below, AC||BD and CE || DF. If OA = 12 cm, AB = 9 cm, OC = 8 cm, and EF = 4.5 cm, find OE.

(3 Marks)

Answer 1

Given that, in ΔOBD, AC ∣∣ BD, OA = 12 cm, AB = 9 cm, and OC = 8 cm.
To find out: The length of OE.
Use the basic proportionality theorem in ΔOBD, we get,
$\frac{OA}{BA}=\frac{OC}{DC}$
$\frac{12}{9}=\frac{8}{DC}$
$DC=6cm$ (1 Mark)
Use the basic proportionality theorem in ΔODF, we get,
$\frac{OC}{DC}=\frac{OE}{EF}$
$\frac{8}{6}=\frac{OE}{4.5}$
$OE=6cm$ (2 Marks)