Question

Cho tam giác ABC có AB = 24 cm. Nếu D nằm trên cạnh AC sao cho \(\widehat{ABC}=\widehat{BDC}\), AD = 7 cm, DC = 9 cm thì BD = ...

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Nhớ giải chi tiết

Answer 1

Ta có \(\Delta CAB\sim\Delta CDB\left(g.g\right)\Rightarrow\dfrac{CB}{CD}=\dfrac{CA}{CB}\)

\(\Rightarrow CB^2=CD\cdot CA\)

Ta có \(CA=CD+DA=16\left(cm\right)\)

\(\Rightarrow CB^2=9\cdot16=144\Rightarrow CB=12\left(cm\right)\)

Ta có \(\dfrac{DB}{BA}=\dfrac{CB}{CA}=\dfrac{12}{16}=\dfrac{3}{4}\)

\(\Rightarrow DB=\dfrac{3}{4}AB=18\left(cm\right)\)