Question

In
Triangle
ABC
B =90, BC² = ACXBD
Then prove that BD is bisector of angle ABC.​

Answer 1

ANSWER:—

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

thanks