If `D` is the mid-point of the side `B C` of triangle `A B C` and `A D` is perpendicular to `A C` , then (a) `3b^2=a^2-c` (b) `3a^2=b^2 3c^2` `b^2=a^2-c^2` (d) `a^2+b^2=5c^2`

Options

A. `3b^(2) = a^(2) - c^(2)`
B. `3a^(2) = b^(2) - 3c^(2)`
C. `b^(2) = a^(2) - c^(2)`
D. `a^(2) + b^(2) = 5c^(2)`

Answer

A

Explanation

From the right -angle `DeltaCAD`, we have

`cos C = (b)/(a//2) rArr (2b)/(a) = (a^(2) + b^(2) -c^(2))/(2ab)`
or `a^(2) + b^(2) - c^(2) = 4b^(2)`
or `a^(2) - c^(2) = 3b^(2)`