Question

AD and BC are two straight lines intersecting at 0. CD and BA are perpendirulars from Band Con AD. If AB=6cm, CD =9cm, AD =20cm and BC=25cm, find the lengths of AO, BO, CO and DO. 

Answer 1

To find : AO , BO , CO , DO

In Δ AOB and Δ COD

∠OAB = ∠ ODC  (90° each)

∠ AOB = ∠ DOC  (vertically opposite angles)

∴ Δ AOB  ∼ Δ DOC   (AA corollary)

`therefore "AO"/"DO" = "OB"/"OC" = "AB"/"DC"`

`"x"/(20 - "x") = "y"/(25 - "y") = 6/9`

`"x"/(20 - "x") = 2/3  , "y"/(25 - "y") = 2/3`

3x = 40 - 2x , 3y = 50 - 2y

5x = 40 , 5y = 50

x = 8 , y = 10

AO = 8 xm , OB = 10 cm

OD = 20 - 8 = 12 cm , OC = 25 - 10 = 15 cm