Math, asked by 12345512, 1 year ago

ABC is a triangle in which angle abc <90 and ADperpendicular to BC. prove that AC square= AB square + BC square - 2 BC× BD

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Samu731: Solution: In triangle ABD;
AB2=AD2+BD2AB2=AD2+BD2 …….. (1)
In triangle ADC;
AC2=AD2+DC2AC2=AD2+DC2
Or, AC2=AD2+(BC–BD)2AC2=AD2+(BC–BD)2
=AD2+BD2+BC2–2BC.BD=AD2+BD2+BC2–2BC.BD……… (2)
Substituting the value of AB2 from equation (1) in equation (2), we get;
AC2=AB2+BC2–2BC.BDAC2=AB2+BC2–2BC.BDproved

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Samu731: Proof: SinceADB is a right triangle, right angled at D, therefore, by Pythagoras theorem,
………(i)
Again,ADB is a right triangle, right angled at D, therefore, by Pythagoras theorem,

– 2BC.BD
– 2DB.BC
– 2DB.BC

Samu731: another method

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Samu731: Most Welcome :-)

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Answers

Answered by samalakankshya7

Answer:check below

Step-by-step explanation:

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