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In the given figure, ABC is a triangle in which AB=AC.P is a point on the side BC such that PM⊥AB and PN⊥AC. Prove that BM×NP=CN×MP.

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In the  figure, it is given that AB=AC and p is a point somewhere on BC such that PM⊥AB and PN⊥AC and we have been asked to prove that BM×NP=CN×MP using the properties of similarities

ML Aggarwal, Avichal publication, class 10, Similarity, chapter 13, question no 11


1 Answer

  1. From the question it is given that, ABC is a triangle in which AB=AC.
    P is a point on the side BC such that PMAB and PNAC.
    We have to prove that, BM×NP=CN×MP
    Consider the ABC
    AB=AC … [from the question]
    B=C … [angles opposite to equal sides]
    Then, consider BMP and CNP
    Therefore, BMPCNP
    So, BM/CN=MP/NP
    By cross multiplication we get,
    Hence it is proved.

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