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In the adjoining figure, AB = AC. If PM ⊥ AB and PN ⊥ AP, show that PM × PC = PN × PB.

In the adjoining figure, AB = AC. If PM ⊥ AB and PN ⊥ AP, show that PM × PC = PN × PB. Similarity, ML Aggarwal Understanding Mathematics Solutions ICSE Class 10.

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Answer

Considering △PNC and △PMB,

∠PNC = ∠PMB (Both are equal to 90°)

∠NCP = ∠PBM (As AB = AC)

Hence by AA axiom △PNC ~ △PMB.

Since, triangles are similar so ratio of their corresponding sides will be equal.

⇒PCPB=PNPM⇒PC×PM=PN×PB.\Rightarrow \dfrac{PC}{PB} = \dfrac{PN}{PM} \\[1em] \Rightarrow PC \times PM = PN \times PB.

Hence, proved that PC × PM = PN × PB.

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