Smile 發問於 科學及數學數學 · 2 月前

Maths problem, how to do (b), thanks?

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  • 2 月前
    最愛解答

    (b)

    [First analyze the statement to be proved.]

    BE² = AC × DC - EC²

    ⇔ BE² + EC² = AC × DC

    Here the left-hand side is actually BC² by Pythagoras theorem.

    Therefore, we are actually asked to prove

    EC² = AC × DC,

    then it is a clear similar triangle setting.

    [The above is the thinking process. Then we proceed to show the work.]

    From (a), it is proved that ΔABC ~ ΔBDC.

    Then,

    AC/BC = BC/DC (corr. sides, ~Δs)

    BC² = AC × DC

    BE² + EC² = AC × DC (Pyth. thm.)

    BE² = AC × DC - EC²

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