Отрезок AD-биссектриса треугольника ABC, в котором угол C=90, AB=15 см и AC=12 см. Найдите BD и CD.

Отрезок AD-биссектриса треугольника ABC, в котором угол C=90, AB=15 см и AC=12 см. Найдите BD и CD.
- Предмет:
  Геометрия
- Автор:
  dutchess
- 5 лет назад

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В прямоугольном треугольнике АВС найдем катет ВС по Пифагору.ВС=√(АВ²-АС²)=√(15²-12²)=9 см.Биссектриса угла треугольника делит противоположную сторону в отношении, равном отношению двух прилежащих сторон.В нашем случае: СD/DB=12/15=4/5. То есть катет ВС делится на 9 частей, ВD=5 частей, СD=4 части. CВ=9, значит СD=CB*4/9=4cм, а ВD=9*5/9=5см.Ответ: ВD=5см, СD=4см.
- Автор:
  hankayala
- 5 лет назад
- 0
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