Question

Triangle ABC is an obtuse triangle , obtuse angled at B.If AD is perpendicular to CB(produced). Prove that AC^2=AB^2+BC^2+2BC.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 :)

Answer 2

Step-by-step explanation:

this is the answer.......