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Rajan@2021
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In △ABC,∠A is acute. BD and CE are perpendicular on AC and AB respectively. Prove that AB×AE=AC×AD.

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One of the basic question from similarity chapter in which we have been asked to prove that ratio of two sides of triangle are equal.

ML Aggarwal Avichal Publication, chapter 13, question no 14

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  1. Consider the ABC,
    So, we have to prove that, AB×AE=AC×AD
    Now, consider the ADB and AEC,
    A=A [common angle for both triangles]
    ADB=AEC [both angles are equal to 90]
    ADBAEC
    So, AB/AC=AD/AE
    By cross multiplication we get,
    AB×AE=AC×AD.

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