Smile 發問於 科學及數學數學 · 4 月前

Maths problem: how to fo, thanks?

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    4 月前
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    Question:

    In ΔABC as shown, C is a point on BD such that AC is an altitude of ΔABD. E is a point on AD such that BE is the angle bisector of ∠ABD. AC and BE intersect at F. ∠BAD = 74° and ∠ADB = 52°. Find ∠EFC.

    https://s.yimg.com/tr/i/49624882f92c4fb09bc52cea67...

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    Solution:

    ∵ AC is an altitude of ΔABD and BE is the angle bisector of ∠ABD

    ∠EFC

    = ∠ACB + ∠DBE ...... ( ext. ∠ of Δ )

    = 90° + (180° - 74° - 52°)/2 ...... ( ∠ sum of Δ )

    = 117°

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    Remarks:

    AC is an altitude of ΔABD ⇒ AC⊥BD

    BE is the angle bisector of ∠ABD ⇒ ∠ABE = ∠DBE

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