Complex Numbers Triangle Inequality

Consider the following two statements :
Statement I : For any two non-zero complex numbers z1,z2
(|z1|+|z2|)|‌

z1

|z1|

+‌

z2

|z2|

|≤2(|z1|+|z2|) and
Statement II : If x,y,z are three distinct complex numbers and a,b,c are three positive real numbers such that ‌

a

|y−z|

=‌

b

|z−x|

=‌

c

|x−y|

, then
‌

a2

y−z

+‌

p2

z−x

+‌

c2

x−y

=1‌. ‌
Between the above two statements,