The perimeter$\ ( in\ cm)$ of a square circumscribing a circle of radius a cm, is:

$( A) \ 8a$
$( B) \ 4a$
$( C) \ 2a$
$( D) \ 16a$

Academic Mathematics NCERT Class 10

Given: A circle with radius a cm and a square circumscribing the circle.

To do: To find out the perimeter of the square in cm.

Solution:

Here we draw a figure, a circle of radius a with centre O. and a square ABCD circumscribing the circle.

Let us say that the circumscribing square touches the circle on P, Q, R and S.

Then$\ OP=OQ=OR=OS=a\ cm$

$\therefore \ OP\bot AD,\ OQ\bot AB,\ OS\bot BC\ $and $OR\bot CD.$

And $PS=OP+OS=a+a=2a$ and here $PS=AB=2a$

$\therefore$ Perimeter of a square$A=4\times 2a\ =8a\ cm$

Option $( A)$ is correct.

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Updated on: 10-Oct-2022

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