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  • In Fig., if angle A = angle C, AB = 6 cm, BP = 15 cm, AP = 12 cm and CP = 4 cm, then find the lengths of PD and CD.

In Fig., if $\angle A=\angle C, A B=6 \mathrm{~cm}, B P=15 \mathrm{~cm}, A P=12 \mathrm{~cm}$ and $C P=4 \mathrm{~cm}$ then find the lengths of PD and CD .

Answers (1)

Given

$
\begin{aligned}
& \therefore A=\angle C, A B=6 \mathrm{~cm}, B P=15 \mathrm{~cm} \\
& \mathrm{AP}=12 \mathrm{~cm} \text { and } \mathrm{CP}=4 \mathrm{~cm} \\
& \text { In } \triangle A P B \text { and } \triangle C P D \\
& \angle A=\angle C \\
& \angle A P B=\angle D P C \text { (Vertically opposite angle) } \\
& \therefore \triangle A P B \sim \triangle C P D \text { [by AA similarity criterion] } \\
& \Rightarrow \frac{A P}{C P}=\frac{P B}{P D}=\frac{A B}{C D} \\
& \frac{12}{4}=\frac{15}{P D}=\frac{6}{C D}
\end{aligned}
$

On taking first and second terms we get

$
\begin{aligned}
& P D=\frac{15 \times 4}{12} \\
& P D=5 \mathrm{~cm}
\end{aligned}
$
On taking the first and last term we get

$
\begin{aligned}
& \frac{12}{4}=\frac{6}{C D} \\
& C D=\frac{6 \times 4}{12} \\
& C D=2 \mathrm{~cm}
\end{aligned}
$

Posted by

infoexpert23

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