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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.
Sum
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Solution
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
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