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Properties of Triangle question

2016 · Shift 1 · Q25

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JEE Advanced
Mathematics
Properties of Triangle
2016 · Shift 1 · Q25

Properties of Triangle question

2016 · Shift 1 · Q25

JEE AdvancedMathematicsProperties of TriangleMultiple correct+4 / −2

In a triangle

\Delta XYZ

, let

x, y, z

be the lengths of sides opposite to the angles

X, Y, Z

respectively, and

2s = x + y + z

. If

{{s - x} \over 4} = {{s - y} \over 3} = {{s - z} \over 2}

and area of incircle of the triangle

XYZ

is

{{8\pi } \over 3}

, then

A
area of the triangle $XYZ$ is $6\sqrt 6$
B
the radius of circumcircle of the triangle $XYZ$ is ${{35} \over 6}\sqrt 6$
C
$\sin {X \over 2}\sin {Y \over 2}\sin {Z \over 2} = {4 \over {35}}$
D
${\sin ^2}\left( {{{X + Y} \over 2}} \right) = {3 \over 5}$

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