Question

in triange abc angleB is abtuse angle d=90 prove that ac²= ab²+bc²+ 2ab*bd

Answer 1

In the right angle triangle ABD, we have 
         AD² = AB² - BD²
In the right angle triangle  ACD we have 
        AD² = AC² - CD²

So    AC² - CD²  = AB² - BD²
        =>  AC² = AB² + CD²  -  BD²
        =>         = AB² + (CD + BD)* (CD - BD )
                     = AB² + BC * [(BC - BD) - BD]
                     = AB² + BC * [ BC - 2 BD ]
                       = AB² +BC² - 2 BC * BD

Hope This Helps :)

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