if s(s-c)=(s-a)(s-b), then what is special about the triangleABC?
s = 0.5(a+b+c)
Please Help Me
maths f.5
2010-08-13 6:52 am
回答 (1)
2010-08-13 7:21 am
✔ 最佳答案
s(s-c)=(s-a)(s-b) 0.5(a+b+c)[0.5(a+b+c) - c] = [0.5(a+b+c) - a] [0.5(a+b+c) - b]0.25(a+b+c)^2 - 0.5(a+b+c)c = 0.25(a+b+c)^2 - 0.5(a+b+c)(a+b) + ab0.5(a+b+c)(a+b) - 0.5(a+b+c)c = ab(a+b+c)(a+b - c) = 2ab(a+b)^2 - c^2 = 2aba^2 + 2ab + b^2 - c^2 = 2aba^2 + b^2 = c^2△ABC is a right angle triangle.
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原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20100812000051KK02008