Q2 of 18 Page 157

Calculate the perimeter of a square with vertices on a circle of diameter 1 centimetre.

The figure is shown below:



The square ABCD is inscribed within the circle.


Diameter of circle, DB = 1 cm


∴ Radius of circle = cm = 0.5 cm


As seen in figure,


Diameter of circle = side of square


∴ the diagonal of the square = 1 cm


For a square,


If side = “s” cm, then,



Diagonal of square, AC2 = s2 + s2


⇒ AC2 = 2s2


⇒ AC = √2 = 1


∴ a =


Perimeter of a square = 4 × Side of square


=


=


=


More from this chapter

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1

Prove that the circumcentre of an equilateral triangle is the same as its centroid.

i) Calculate the length of side of an equilateral triangle with vertices on a circle of diameter 1 centimetre.


ii) Calculate the perimeter of such a triangle.

 3

Calculate perimeter of a regular hexagon with vertices on a circle of diameter 1 centimetre.

 1

The perimeter of a regular hexagon with vertices on a circle is 24 centimetres.

i) What is the perimeter of a square with vertices on this circle?


ii) What is the perimeter of a square with vertices on a circle of double the diameter?


iii) What is the perimeter of an equilateral triangle with vertices on a circle of half the diameter of the first circle?

 2

A wire was bent into a circle of diameter 4 centimetres. What would be the diameter of a circle made by bending a wire of half the length?