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Which of the following statements is/are true? A: If a circle is formed from a wire, which was initially in the shape of a semi-circle, then ratio of radius of circle and that of semi-circle will be 7: 11. B: If in a semi-circle of radius ‘r’, another semi-circle of radius ‘4r/5’ is drawn, then area of the remaining part of larger semi-circle will be ‘3πr2/5’. C: In a circle of radius ‘r’, if ‘O’ is the center of circle and radii OA and OB are at the angle of 45°, then the length of major arc AB will be ‘7πr/8’.

Which of the following statements is/are true? A: If a circle is formed from a wire, which was initially in the shape of a semi-circle, then ratio of radius of circle and that of semi-circle will be 7: 11. B: If in a semi-circle of radius ‘r’, another semi-circle of radius ‘4r/5’ is drawn, then area of the remaining part of larger semi-circle will be ‘3πr2/5’. C: In a circle of radius ‘r’, if ‘O’ is the center of circle and radii OA and OB are at the angle of 45°, then the length of major arc AB will be ‘7πr/8’. Correct Answer None

GIVEN:

Three statement.

CONCEPT:

Properties of circle and semi-circle.

FORMULA USED:

Perimeter of semi-circle = (πr + 2r)

Circumference of circle = 2πR

CALCULATION:

A: Let the radius of circle is ‘R’ and that of semi-circle is ‘r’.

Since, perimeter of semi-circle will be equal to circumference of circle,

So,

(πr + 2r) = 2πR

⇒ 36r/7 = 44R/7

⇒ R: r = 9: 11.

B: The area of smaller semi-circle = π(4r/5)2 = 16πr2/25

Area of larger semi-circle = πr2.

Area of remaining part of larger semi-circle = πr2 – 16πr2/25 = 9πr2/25

C: Length of major arc AB = 2πr(360° – 45°)/360° = 7πr/4.

∴, none is TRUE.

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