In the figure, triangle ABC is equilateral,AD is an altitude,Oid the circumcentre of the triangle.If AB=18cm,find OA+OB+OC,leaving your answer in surd from.
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maths
2007-08-18 5:30 am
回答 (1)
2007-08-18 6:44 am
✔ 最佳答案
Since O is the circumcentre of ΔABC, OD bisects BC.
i.e. BD = DC = 18 cm / 2 = 9cm
∠BOC = 2∠BAC = 2 (60° ) = 120°
Since ΔBOD ~= ΔCOD (R. H. S.),
∠BOD = ∠COD = 120°/2 = 60°
So OC = DC sin 60° = 9√3/2 cm
As OA = OB = OC (radii),
OA + OB + OC = (9√3/2 + 9√3/2 + 9√3/2) cm = 27√3/2 cm
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