Re: [中學] 國中幾何
其實會用 Stewart's theorem 就可以很快了
http://en.wikipedia.org/wiki/Stewart%27s_theorem
因為 CP : PQ : QB = 3 : 2 : 3
所以設 CP = 3t , PQ = 2t , QB = 3t
根據Stewary's theorem
AB^2 * CQ + AC^2 * BQ = AQ^2 * BC + CQ * BQ * BC
AB^2 * CP + AC^2 * BP = AP^2 * BC + CP * BP * BC
因為CP = BQ , BP = CQ
所以相減得
AB^2 * (CQ - BQ) - AC^2 * (CQ - BQ) = (AQ^2 - AP^2) * BC
256 * 2t = (AQ^2 - AP^2) * 8t
——————
√AQ^2 - AP^2 = 8
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