According to the theorem of Apollonius, if $AD$ is the median to side $BC$ of $\triangle ABC$, then —

• a$AB^2 + AC^2 = 2(AD^2 + BD^2)$
• b$AB^2 + AC^2 = AD^2 + BD^2$
• c$AB^2 - AC^2 = 2(AD^2 - BD^2)$
• d$AB^2 + AC^2 = AD^2 \cdot BD^2$