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?
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?
Updated On: May 22, 2024
- $2 Y=X+Z$
- $Y=X+Z$
- $\tan \frac{X}{2}=\frac{x}{y+z}$
- $x^{2}+z^{2}-y^{2}=x z$
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The Correct Option is B, C
Solution and Explanation
(B) $Y=X+Z$
(C) $\tan \frac{X}{2}=\frac{x}{y+z}$
(C) $\tan \frac{X}{2}=\frac{x}{y+z}$
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