Question 21
In triangle $ABC$, $D$ and $E$ are the midpoints of $AB$ and $AC$, respectively. $DC$ is perpendicular to $BE$. If $AB=16$ and $BC=12$, find $AB^2+BC^2+CA^2$.
Answer format: enter one whole number without units; leading zeros are optional. The source answer sheet uses four digits (for example, 7 is shaded as 0007).
Answer format: enter one whole number without units; leading zeros are optional. The source answer sheet uses four digits (for example, 7 is shaded as 0007).