試解

Suppose the top point isn't a qualified point. Otherwise the problem is already solved. That is, its three edges a,b,c cannot form a triangle. Assume a is larger than b and c. Then a > b+c > y

Meanwhile:  x+ b > a,     z+c >a,      so x+z+b+c> 2a
Remember a > b+c,  so x+z > a      (Eq1)

Remember a > y, so a+z>y+z > x     (Eq2)

Similarly, a+x > y+ x > z        (Eq3)

Combine Eq 123, it turns out a, x, z can form a triangle.