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標題:

A.Maths Problem(Solution of triangles and its application)

發問:

Please go to http://aerodrive.twghwfns.edu.hk/~4s123/Q15.JPG and find the figure. The question:In triangle ABC.D is the mid-point of BC.By considering b and using the Cosine Law,prove that AB^2+AC^2=2AD^2+2CD^2. Thx~~~~

最佳解答:

consider AB,AC AB^2=AD^2+BD^2-2(AD)(BD)cos(180-b) AB^2=AD^2+BD^2+2(AD)(BD)cosb AC^2=AD^2+CD^2-2(AD)(CD)cosb AB^2+AC^2 =AD^2+BD^2+2(AD)(BD)cosb+AD^2+CD^2-2(AD)(CD)cosb =2AD^2+2CD^2 (since CD=BD)

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