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Which of the following statements is/are true? A: In a circle, PQ is a chord and OP and OQ are the radii of the circle. If ∠POQ = 90°, then ratio of the area of triangle POQ and that of circle will be 7: 22. B: Area of a circle is one-fourth of the product of ‘π’ and square of diameter of circle. C: Diameter of a semi-circle is 38(8/9)% of its perimeter.

Which of the following statements is/are true? A: In a circle, PQ is a chord and OP and OQ are the radii of the circle. If ∠POQ = 90°, then ratio of the area of triangle POQ and that of circle will be 7: 22. B: Area of a circle is one-fourth of the product of ‘π’ and square of diameter of circle. C: Diameter of a semi-circle is 38(8/9)% of its perimeter. Correct Answer Only B and C

GIVEN:

Three statements.

CONCEPT:

Properties of chord, radius and area of circle.

FORMULA USED:

Area of triangle = (1/2) × Base × Height

Perimeter of semi-circle = (πr + 2r)

CALCULATION:

A: Let the radius of the circle OP = OQ = r.

Given, ∠POQ = 90°, So the area of triangle POQ will be (1/2) × OP × OQ = r2/2.

The area of the circle = πr2 = (22/7)r2.

Now the ratio of the area of triangle POQ and that of circle = (r2/2): (22/7)r2 = 7: 44.

B: Let diameter of a circle is ‘D’, then its radius (r) = ‘D/2’.

So, area of the circle = πr2 = πD2/4.

C: Let radius of a semicircle be ‘r’, then its diameter will be ‘2r’ and its perimeter will be (πr + 2r) = = 36r/7.

The diameter of semicircle is × 100 = 38(8/9)% of its perimeter.

∴, only B and C are TRUE.

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