Q. 244.9( 8 Votes )
Jaya drew an incircle of a square. That circle is also circumscribe an equilateral triangle of which each length of side of 4√3 cm. Let us write by calculating the length of diagonal of square.
Answer :
Given: Length of side of equilateral triangle = 4√3 cm
Height of equilateral triangle
The centroid of equilateral triangle is at A and lies on height BK.
⇒ BA = 4 cm
So, the radius of the circum circle of this triangle = 4 cm.
Now, diameter of the circle = 2× radius = 8 cm
⇒ IJ = 8 cm
From the figure, IJ = EH = side of the square
⇒ Side of the square = 8 cm
We know that the diagonal of a square =√2× side
⇒ FH = 8√2 cm
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