Question

ABCD is a trapezium such that BC||AD and AB = 4 cm. If the diagonals AC and BD intersect at O such that AO/OC = DO/OB =1/2, then BC =
A. 7 cm
B. 8 cm
C. 9 cm
D. 6 cm

Answer 1

Answer:

answer is option B.............

Answer 2

B. 8 cm

Step-by-step explanation:

Given: BC||AD

AB = 4cm

Diagonals AC and BD intersect at O such that AO/OC = DO/OB =1/2.

To find: BC

Solution

Let BC = m, ∠AOD be x which implies ∠COB = x

∠OAD = y, implies ∠OCB = y

CO = 2a implies OA = a

ΔOAD ~ ΔOCB (AA similarity)

So OA/AD = OC/CB

a/4 = 2a/m

Therefore m = 2a * 4/a = 8 cm

Option B is the answer.