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Question
In figure, if ∠A = ∠C, AB = 6 cm, BP = 15 cm, AP = 12 cm and CP = 4 cm, then find the lengths of PD and CD.
Solution
According to the question,
∠A = ∠C,
AB = 6 cm,
BP = 15 cm,
AP = 12 cm
CP = 4 cm
From ∆APB and ∆CPD,
∠A = ∠C
∠APB = ∠CPD ...[Vertically opposite angles]
∴ By AAA similarity criteria,
ΔAPD ∼ ΔCPD
Using basic proportionality theorem,
⇒ `("AP")/("CP") = ("PB")/("PD") = ("AB")/("CD")` ...[By basic proportionality theorem]
⇒ `12/4 = 15/("PD") = 6/("CD")`
Considering `("AP")/("CP") = ("PB")/("PD")`, we get,
`12/4 = 15/("PD")`
PD = `(15 xx 4)/12`
= `60/12`
= 5 cm
Considering, `("AP")/("CP") = ("AB")/("CD")`
⇒ CD = `((6 xx 4))/12` = 2 cm
Therefore,
Length of PD = 5 cm
Length of CD = 2 cm
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