In ΔABD, C is the midpoint of BD. If AB = 10 cm, AD = 12 cm and AC = 9 cm, then BD = ?

Answer: Option B

$$\begin{array}{rl}& A{B}^2+A{D}^2=2\left(A{C}^2+B{C}^2\right)\\ & 100+144=2\left(81+x^2\right)\\ & \frac{244}{2}=81+x^2\\ & 122-81=x^2\\ & x^2=41\\ & x=\sqrt{41}\\ & BD=2\sqrt{41}\end{array}$$