As shown in the figure, D is a point on the edge BC of △ ABC. Given AB = 13, ad = 12, AC = 15, BD = 5, then the length of BC is______ ．

∵ ad2 + BD2 = 144 + 25 = 169, AB2 = 169, ∵ ad2 + BD2 = AB2 ≁ ad ⊥ BC (Pythagorean inverse theorem), ∵ ADC = 90 °, ∵ CD = ac2 − ad2 = 152 − 122 = 9, ∵ BC = CD + BD = 5 + 9 = 14

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