The length of the diameter of the circle circumscribed about this triangle is [tex]16/\sqrt{3} cm[/tex].
Vertex angle of isosceles triangle =120°
So, semi-vertex angle of isosceles triangle = 60°
The third side of the triangle =8cm
Suppose the equal sides =a
What is an isosceles triangle?
A triangle with two of its sides equal to each other is called an isosceles triangle.
We know that altitude drawn from the vertex in an isosceles triangle bisects the opposite side.
So, Sin(semi vertex angle) = 8/one of equal side
[tex]sin60 =4/a\\\frac{\sqrt{3} }{2} =4/a\\a=8/\sqrt{3}[/tex]
So, equal sides = 8/√3 cm each
As we know [tex]Sin(vertex Angle)/Opposite side = 1/2R[/tex]
Where R is the circumradius of the triangle
So, 2R =[tex]\frac{oppositeSide}{sin(vertexAngle)}[/tex]
[tex]2R=8/sin120\\2R=16/\sqrt{3}[/tex]
Hence, the length of the diameter of the circle circumscribed about this triangle is [tex]16/\sqrt{3} cm[/tex].
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