In the given figure, the centre of all three circles of equal radius = 10 cm lie in a straight line. These circles are inscribed in a rectangle which is inscribed in another circle.

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Solution

Q.
In the given figure, the centre of all three circles of equal radius = 10 cm lie in a straight line. These circles are inscribed in a rectangle which is inscribed in another circle.

(i) The area of largest circle is $1000 π c m^{2} .$

(ii) The area of largest circle is $900 π c m^{2} .$

(iii) Area of rectangle is $1200 c m^{2}$ .

(iv) Perimeter of rectangle is 80 cm.

Which of the above statements are correct

1 (i) and (iv)

2 (ii) and (iv)

3 (ii) and (iii)

4 (i) and (iii)

Ans.
(4)

Length of rectangle (AC), l = sum of diameter of all inner circles

$= 3 \times 20 = 60 cm Width of rectangle BC, b = diameter of smaller circle = 20 cm Radius of bigger circle (OB), Diagonal of Rectangle R = \frac{\sqrt{{AC}^{2} + {BC}^{2}}}{2} = \frac{\sqrt{(60)^{2} + (20)^{2}}}{2} = \frac{\sqrt{4000}}{2} = \frac{\sqrt{1000}}{1} Area of rectangle = l \times b = 60 \times 20 = 1200 {cm}^{2} ∴ Statement (iii) is correct . = 2 (l + b) = 2 (60 + 20) = 160 cm ∴ Statement (iv) is incorrect . Area of bigger circle = {πR}^{2} = π \times (\sqrt{1000})^{2} = 1000 π {cm}^{2} ∴ Statement (i) is correct . Option (d) is correct .$

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