A3. Trapezoid $A B C D$ has bases of lengths $|A B|=120 \mathrm{~mm}$ and $|C D|=30 \mathrm{~mm}$ and right angles at vertices $B$ and $C$. The diagonals of the trapezoid intersect at point $E$. How many millimeters is point $E$ from side $B C$?
(A) 21
(B) 22
(C) 23
(D) 24
(E) 25

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A3. Let $F$ be the orthogonal projection of point $E$ onto side $B C$. Triangles $A B E$ and $C D E$ are similar. The ratio of their sides opposite to vertex $E$ is $|A B|:|C D|=120$ : $30=4: 1$, so the ratio of their heights to these two sides is also $|F B|:|F C|=$ 4 : 1. Triangles $A B C$ and $E F C$ are also similar, and the ratio of their heights through vertex $C$ is $|C B|:|C F|=5: 1$. Therefore, the ratio of their sides opposite to vertex $C$ is also $|A B|:|E F|=5: 1$, and thus $|E F|=\frac{|A B|}{5}=24 \mathrm{~mm}$.