Question

In $△ABC,\overline{AD}$ is a median, hence according to the Apollonius theorem, ............ is true.

• A. ${AB}^2+{AC}^2=2({AD}^2+{BC}^2)$
• B. ${AB}^2+{AC}^2=2({BD}^2+{DC}^2)$
• C. ${AB}^2+{AC}^2=2({AD}^2+{DC}^2)$
• D. ${AB}^2+{AC}^2=2({BD}^2+{BC}^2)$

Answer 1

The correct option is C ${AB}^2+{AC}^2=2({AD}^2+{DC}^2)$

$AD$ is the median and is perpendicular to $BC$

$⟹AD$ is the perpendicular form $A$ to $BC$ which divides $BC$ into two equal parts

$\therefore BD=DC$

$⟹D$ is the midpoint of $BC$

Then according to the Apollonius theorem,

${AB}^2+{AC}^2=2[{AD}^2+{DC}^2]$