Question

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 $\tan \frac{x}{2}+\tan \frac{z}{2}=\frac{2 y}{x+y+z}$ then which of the following statements is/are TRUE?

• A. $2 Y=X+Z$
• B. $Y=X+Z$
• C. $\tan \frac{X}{2}=\frac{x}{y+z}$
• D. $x^{2}+z^{2}-y^{2}=x z$

Answer 1

The Correct Option is B, C

(B) $Y=X+Z$
(C) $\tan \frac{X}{2}=\frac{x}{y+z}$