Chapter 15. Circles NIOS Class 10 Mathematics Chapter-Wise Important Questions and Answers

Chapter 15. CIRCLES

Optional Questions and Answers for Algebraic Expressions and Polynomials [1 Mark]

CHECK YOUR PROGRESS 3.1

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Long Questions and Answers for Algebraic Expressions and Polynomials [ 3 or 4 Mark]

CHECK YOUR PROGRESS 15.1

In questions 1 to 5, fill in the blanks to make each of the statements true.

1. In Fig. 15.25,

(i) AB is a ... of the circle.

(ii) Minor arc corresponding to AB is... .

Answer: (i) AB is a chord of the circle.

(ii) Minor arc corresponding to AB is APB .

2. A ... is the longest chord of a circle.

Answer: A diameter is the longest chord of a circle.

3. The ratio of the circumference to the diameter of a circle is always ... .

Answer: The ratio of the circumference to the diameter of a circle is always constant .

4. The value of π as 3.1416 was given by great Indian Mathematician... .

Answer: The value of π as 3.1416 was given by great Indian Mathematician aryabhata-I

5. Circles having the same centre are called ... circles.

Answer: Circles having the same centre are called concentric circles.

6. Diameter of a circle is 30 cm. If the length of a chord is 20 cm, find the distance of the chord from the centre.

Solution: Here, AB = 30 cm , OA=OB =OC=AB2=302=15 cm

, CD=20 cm and CM=DM=12CD=202=10 cm

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In ∆OCM , we have

OM2+CM2=OC2

⇒OM2=OC2-CM2

⇒OM=152-102=225-100=125=5²×5

⇒OM=55cm

Therefore, the distance of the chord from the centre is 55cm .

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