italy-esame-di-stato 2023 Q1

italy-esame-di-stato · Other · esame-di-stato__matematica Proof Direct Proof of a Stated Identity or Equality
Let $ABC$ be a right triangle with right angle at $A$. Let $O$ be the center of the square $BCDE$ constructed on the hypotenuse, on the opposite side from vertex $A$.
Prove that $O$ is equidistant from the lines $AB$ and $AC$.
Let $ABC$ be a right triangle with right angle at $A$. Let $O$ be the center of the square $BCDE$ constructed on the hypotenuse, on the opposite side from vertex $A$.

Prove that $O$ is equidistant from the lines $AB$ and $AC$.