4. In the trapezoid $A B C D$, the following holds

$$
A B=12, B C=7, C D=8 \text { and } \measuredangle A B C=90^{\circ} .
$$

Does the bisector of the interior $\Varangle D A B$ intersect the leg $B C$ or the base $C D$?
Solution. Let $C'$ be the point where the bisector of $\measuredangle DAB$ intersects the line $DC$. If $DC' > 8$,

then $DC' > DC$, so the bisector of $\measuredangle DAB$ intersects the side $BC$.