6. (BUL) An isosceles trapezoid with bases $a$ and $b$ and height $h$ is given. (a) On the line of symmetry construct the point $P$ such that both (nonbase) sides are seen from $P$ with an angle of $90^{\circ}$. (b) Find the distance of $P$ from one of the bases of the trapezoid. (c) Under what conditions for $a, b$, and $h$ can the point $P$ be constructed (analyze all possible cases)?
6. Let $E, F$ respectively be the midpoints of the bases $A B, C D$ of the isosceles trapezoid $A B C D$. (a) The point $P$ is on the intersection of $E F$ and the circle with diameter $B C$. (b) Let $x=E P$. Since $\triangle B E P \sim \triangle P F C$, we have $x(h-x)=a b / 4 \Rightarrow$ $x_{1,2}=\left(h \pm \sqrt{h^{2}-a b}\right) / 2$. (c) If $h^{2}>a b$ there are two solutions, if $h^{2}=a b$ there is only one solution, and if $h^{2}<a b$ there are no solutions.