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Dear student,

By basic proportionality theorem

\frac{A D}{D B} = \frac{A E}{E P} \frac{4}{4} = \frac{A E}{E P}

EP=AE

now AP= $\frac{1}{2}$ PC

but AP= $\frac{1}{2}$ AE

PC=AE

AE=3=PC
Thus proved
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Aakash EduTech Pvt. Ltd.

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