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Will it be true to say that the perimeter of a square circumscribing a circle of radius \[a\] cm is \[8a\]cm? Give reasons for your answer.
Will it be true to say that the perimeter of a square circumscribing a circle of radius \[a\] cm is \[8a\]cm? Give reasons for your answer.
Areas Related to Circles | Exercise 11.2 | Maths | NCERT Exemplar
Will it be true to say that the perimeter of a square circumscribing a circle of radius \[a\] cm is \[8a\]cm? Give reasons for your answer.

The given statement is true

Explanation:

Let \[r\] be the radius of circle and is equal \[a\] cm

Therefore, Diameter of the circle = d = \[2\times Radius\] = \[2a\] cm

From the question we got that  circle is inscribed in the square,

Therefore, Side of a square = Diameter of circle = \[2a\] cm

Perimeter of a square = \[4\times (side)\] = \[4\times 2a\] = \[8a\] cm

Therefore, the perimeter of a square circumscribing a circle of radius \[a\] cm is \[8a\] cm.

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More Material

(i) Consider a thin lens placed between a source (S) and an observer (O). Let the thickness of the lens vary as 2 0 () – α = b wb w, where b is the verticle distance from the pole. w0 is a constant. Using Fermat’s principle i.e. the time of transit for a ray between the source and observer is an extremum, find the condition that all paraxial rays starting from the source will converge at a point O on the axis. Find the focal length.
(ii) A gravitational lens may be assumed to have a varying width of the form w(b) = k1 ln (k2/b) = k1 ln (k2/bmin). Show that an observer will see an image of a point object as a ring about the centre of the lens with an angular radius.
β = √(n-1)k1 u/v / u + v

If light passes near a massive object, the gravitational interaction causes a bending of the ray. This can be thought of as happening due to a change in the effective refractive index of the medium given by n(r) = 1 + 2 GM/rc2 where r is the distance of the point of consideration from the centre of the mass of the massive body, G is the universal gravitational constant, M the mass of the body and c the speed of light in vacuum. Considering a spherical object find the deviation of the ray from the original path as it grazes the object.