Let 𝑥, 𝑦 and 𝑧 be positive real numbers. Suppose 𝑥, 𝑦 and 𝑧 are the lengths of the sides of a triangle
opposite to its angles 𝑋, 𝑌 and 𝑍, respectively. If

$$\tan \frac{X}{2} + \tan \frac{Z}{2} = \frac{2y}{x + y + z}$$,

then which of the following statements is/are TRUE?

A

2Y = x + Z

B

Y = x + Z

C

$$\tan \frac{X}{2} = \frac{X}{Y + z}$$

D

$$x^{2} + z^{2} + y^{2} = xz$$