已知圓內接四邊形 各邊長 ab線段等於3 bc線段等於3 cd線段等於5 da線段等於8 請問此圓的半徑等於多少?
回答 (1)
2015-10-08 9:34 pm
圓內接四邊形, AB=BC=3, CD=5, DA=8, 半徑r=?
Cosine Law:
AC^2 = 9 + 9 - 18cosB = 25 + 64 - 80cosD
18 - 18cosB = 89 - cos(180 - B) = 89 + 80cosB
=> 89cosB = -71
=> cosB = -71/89
=> B = 136.4264°
O = Center
OH⊥BC
ΔOBC: BH = HC = 1.5, OA = OB = OC = r
∠OBC = ∠OBA = 136.426/2 = 68.2132°
=> r = 1.5/cos68.2132° = 4.04145.....Answer
Cosine Law:
AC^2 = 9 + 9 - 18cosB = 25 + 64 - 80cosD
18 - 18cosB = 89 - cos(180 - B) = 89 + 80cosB
=> 89cosB = -71
=> cosB = -71/89
=> B = 136.4264°
O = Center
OH⊥BC
ΔOBC: BH = HC = 1.5, OA = OB = OC = r
∠OBC = ∠OBA = 136.426/2 = 68.2132°
=> r = 1.5/cos68.2132° = 4.04145.....Answer
收錄日期: 2021-04-30 20:07:02
原文連結 [永久失效]:
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