Question

In the given figure AD is perpendicular to BC produced, prove that :
`c^(2)=a^(2)+b^(2)=2ax`

Answer 1

In right angled `triangleABD`, using pythagoras theorem , we have
`AB^(2)= BD^(2)+AD^(2)` ltbr `Rightarrow " " c^(2)(a+x)^(2)+h^(2)`
`c^(2)=a^(2)+2ax+x^(2)+h^(2)`
`c^(2)=a ^(2) +2ax+ b^(2) " "( h^(2)+x^(2)=b^(2))`