Vector

Since ABCD is a parallelogram, vector AD = vector BC (parallel and of same length)
Now vector OC = vector OB + vector BC
c = b + vector BC
a + c = a + b + vector BC ... (1)
vector OD = vector OA + vector AD
d = a + vector AD
b + d = a + b + vector AD ... (2)
Since vector AD = vector BC, so (1) = (2)
=> a + c = b + d ... (3)
Let E be the mid point of AC and F the mid point of BD
Therefore vector OE = (vector OA + vector OC)/2 = (a + c)/2 ... (4)
vector OF = (vector OB + vector OD)/2 = (b + d)/2 ... (5)
From (3), we conclude that (4) = (5)
Therefore vector OE = vector OF and therefore E and F is a same point.
It follows that the 2 diagonals of the parallelogram bisects each other.

We know AC=BD and AB=CD, so arc BAC= arc BDC ,
arc ACB = arc BCD, amd also arc ABC= arc CBD. Then line up
point B and C, you will find triangle ABC equal to triangle BCD,
they are the same.