A3. Triangle $A B C$ is an isosceles right triangle with a right angle at vertex $A$. On side $B C$ lies a point $D$,

![](https://cdn.mathpix.com/cropped/2024_06_07_ec35f4a613e63419eaedg-04.jpg?height=375&width=585&top_left_y=1183&top_left_x=1335)
such that $A D$ is the median of triangle $A B C$. Which of the segments is as long as segment $A D$?
(A) $A C$
(B) $A B$
(C) $B C$
(D) $B D$
(E) None of the above.
A3. We find that an isosceles right triangle is half of a square with side $a$ and that the hypotenuse is the diagonal of this square. The median $P T$ bisects the hypotenuse and, due to the equal legs, is also perpendicular to it. From this, we can see that the median is half the diagonal of the square. Thus, its length is the same as the length of the segments $Q T$ or $R T$.