Construct the triangle with given points and lines

Question

On the following picture you see the excersice handed to us. Construct triangle ABC when you know that x is the line that contains points B and C, line z is the median that goes trough point A and point E is the start of the altitude going through point B. How can you construct the triangle when this is all thats given? Please explain the method! (ps The pink obviously shows the triangle but thats not given in the actual excercise)

Answer 1

$\triangle BEC$ is a right-angled triangle with $B$ and $C$ equidistant from $O$, the intersection of the two lines - which, since they are also the diameter of a circle with $E$ on the circumference, means that $|EO| = |BO|=|CO|$. Having established $B$ and $C$, the line from $C$ through $E$ gives $A$ at the intersection with $z$.

Answer 2

Let $F$ be the intersection point of $x$ with $z$.

Then, draw a circle whose center is $F$ with radius $EF$. The intersection points of the circle with $x$ are $B,C$. Now extend the sides of the right triangle $\triangle{BCE}$ to have $A$.