According to Ptolemy's theorem
1
Every triangle with two angle bisectors of equal lengths is isosceles.
2
The sum of squares of any of the two sides of a triangle equals to twice its square on half of the third side, along with the twice of its square on the median bisecting the third side
3
In a cyclic quadrilateral, the product of the lengths of its diagonals is equal to the sum of the products of the lengths of the pairs of opposite sides.
4
In a cyclic quadrilateral, the sum of the opposite sides of that quadrilateral is 180°