In trapezium ABCD side `AB||` side DC, diagonals AC and BD intersect In point O. If `AB=20, DC=6, OB=15` thn find OD.

Explanation

Side `AB||` side DC and line DB is the transversal.
`/_CDB~=/_ABD`………….(Alternate angles)
i.e. `/_CDO~=/_ABO`…….`(B-O-D)`……..1
In `DeltaCOD` and `DeltaAOB`,
`/_CDO~=/_ABO` ………….[From 1]
`/_COD~=/_AOB`..(Vertically opposite angles )
`:.DeltaCOD~DeltaAOB`....(AA test of similarity)
`:.(OD)/(OB)=(DC)/(AB)`............(Corresponding sides of similar triangles are in proportion)
`:.(OD)/15=6/20`
`:.ODxx20=15xx6`
`:gtOD=(15xx6)/20`
`:.OD=9/2`
`:.OD=4.5`
`OD=4.5`