Question

ABCD is a trapezium whose BC parallel AD and AD = 4 cm. Diagonals AC and BD are intersected at O in such way that `[AO]/[OC] = [DO]/[OB] = 1/2`, then what is the length of BC?

Answer 1

`BC=8`

Explanation:

Given `BC` parallel to `AD, and AD=4`
Let `BC=m`
Let `angleAOD=x, => angleCOB=x`
Let `angleOAD=y, => angleOCB=y`
Let `CO=2a, => OA=1a`

`=> DeltaOAD, and DeltaOCB` are similar,
`=> (OA)/(AD)=(OC)/(CB)`
`=> (1a)/4=(2a)/m`
`=> m=8`

Hence, `BC=m=8`