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NCERT Solutions for Class 9 Maths Chapter 10 Circles
NCERT Solutions for Class 9 Maths Chapter 10 Circles are prepared by CBSE student eCARE expert to score good marks in class 9. This chapter contain many topics which are very important to score good in class 9. There are some important topic/Activity mentioned below:
Fill in the blanks.
(i) The centre of a circle lies in ___ of the circle. (exterior/interior)
(ii) A point, whose distance from the centre of a circle is greater than its radius lies in ____ of the circle, (exterior/interior)
(iii) The longest chord of a circle is a ____ of the circle.
(iv) An arc is a ____ when its ends are the ends of a diameter.
(v) Segment of a circle is the region between an arc and ____ of the circle.
(vi) A circle divides the plane, on which it lies, in ____ parts.
Solution:
(i) interior
(ii) exterior
(iii) diameter
(iv) semicircle
(v) the chord
(vi) three
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Some questions are asked by class 9 students related to Maths
Question 1.
Recall that two circles are congruent, if they have the same radii. Prove that equal chords of congruent circles subtend equal angles at their centres
Solution:
Given: Two congruent circles with centres O and O’ and radii r, which have chords AB and CD respectively such that AB = CD.
To Prove: ∠AOB = ∠CO’D
Proof: In ?AOB and ?CO’D, we have
AB = CD [Given]
OA = O’C [Each equal to r]
OB = O’D [Each equal to r]
∴ ?AOB ≅ ?CO’D [By SSS congruence criteria]
⇒ ∠AOB = ∠CO’D [C.P.C.T.]
Ex 10.2 Class 9 Maths Question 2.
Prove that, if chords of congruent circles subtend equal angles at their centres, then the chords are equal.
Solution:
Given: Two congruent circles with centres O & O’ and radii r which have chords AB and CD respectively such that ∠AOB = ∠CO’D.
To Prove: AB = CD
Proof: In ?AOB and ?CO’D, we have
OA = O’C [Each equal to r]
OB = O’D [Each equal to r]
∠AOB = ∠CO’D [Given]
∴ ?AOB ≅ ?CO’D [By SAS congruence criteria]
Hence, AB = CD [C.P.C.T.]