Question 3 In Fig. 6.58, ABC is a triangle in which ABC > 90 and AD CB produced. Prove that AC2 = AB2 + BC2 + 2 BC . BD. Given : ABC is a triangle in which ABC > 90 and AD CB extended D. To Prove: AC2 = AB2 + BC2 + 2BC.BD Proof: In right ADB Applying Pythagoras theorem, AB2 = AD2 + BD2 In right ADC Applying Pythagoras theorem, AC2 = AD2 + CD2 From (2) AC2 = AD2 + CD2 AC2 = AD2 + (BD + BC)2 AC2 = AD2 + BD2 + BC2 + 2BD.BC Put AD2 + BD2 = AB2 from equation (1) AC2 = AB2 + BC2 + 2BC.BD. Hence Proved.

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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