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Properties of Triangle question

2020 · Shift 1 · Q28

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JEE Advanced
Mathematics
Properties of Triangle
2020 · Shift 1 · Q28

Properties of Triangle question

2020 · Shift 1 · Q28

JEE AdvancedMathematicsProperties of TriangleMultiple correct+4 / −2

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 {X \over 2} + \tan {Z \over 2} = {{2y} \over {x + y + z}}

, then which of the following statements is/are TRUE?

A
2Y = X + Z
B
Y = X + Z
C
$\tan {X \over 2}$ = ${x \over {y + z}}$
D
x2 + z2 $-$ y2 = xz

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