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单词 ProofOfApolloniusTheorem1
释义

proof of Apollonius theorem


Let m be a median of the triangle, as shown in the figure.

By Stewart’s theorem we have

a(m2+(a2)2)=b2(a2)+c2(a2)

and thus

m2+(a2)2=b2+c22.

Multiplying both sides by 2 gives

2m2+a22=b2+c2.

QED

Titleproof of Apollonius theoremPlanetmathPlanetmath
Canonical nameProofOfApolloniusTheorem1
Date of creation2013-03-22 12:41:20
Last modified on2013-03-22 12:41:20
Ownerdrini (3)
Last modified bydrini (3)
Numerical id5
Authordrini (3)
Entry typeProof
Classificationmsc 51-00
Related topicMedian
Related topicCevian
Related topicApolloniusTheorem
Related topicStewartsTheorem
Related topicProofOfStewartsTheorem
Related topicProofOfApolloniusTheorem
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更新时间:2025/5/4 13:34:42