NCERT Solutions for Class 9 Maths Chapter 10 Circles (वृत) Exercise 10.1 or Exercise 10.2 or Exercise 10.3 or Exercise 10.4 or Exercise 10.5 or Exercise 10.6 in English Medium or प्रश्नावली 10.1 or प्रश्नावली 10.2 or प्रश्नावली 10.3 or प्रश्नावली 10.4 or प्रश्नावली 10.5 or प्रश्नावली 10.6 in Hindi Medium to study online or download in PDF form free.
| Class 9: | Maths – गणित |
| Chapter 10: | Circles |
Table of Contents
- 1 NCERT Solutions for Class 9 Maths Chapter 10
- 1.1 Class 9 Maths Chapter 10 Circles – वृत Solutions
- 1.1.1 Hindi and English Medium Solutions
- 1.1.1.1 9 Maths Exercise 10.1 Solutions
- 1.1.1.2 9 Maths Exercise 10.2 Solutions
- 1.1.1.3 9 Maths Exercise 10.3 Solutions
- 1.1.1.4 9 Maths Exercise 10.4 Solutions
- 1.1.1.5 9 Maths Exercise 10.5 Solutions
- 1.1.1.6 9 Maths Exercise 10.6 Solutions
- 1.1.1.7 9 गणित प्रश्नावली 10.1 के हल
- 1.1.1.8 9 गणित प्रश्नावली 10.2 के हल
- 1.1.1.9 9 गणित प्रश्नावली 10.3 के हल
- 1.1.1.10 9 गणित प्रश्नावली 10.4 के हल
- 1.1.1.11 9 गणित प्रश्नावली 10.5 के हल
- 1.1.1.12 9 गणित प्रश्नावली 10.6 के हल
- 1.1.1.13 Important Terms and Theorems on
- 1.1.2 Fill in the blank: The centre of a circle lies in _____________ of the circle.
- 1.1.3 याद कीजिए कि दो वृत्त सर्वांगसम होते हैं, यदि उनकी त्रिज्याएँ बराबर हों। सिद्ध कीजिए कि सर्वांगसम वृत्तों की बराबर त्रिज्याएँ उनके केन्द्रों पर बराबर कोण अंतरित करती हैं।
- 1.1.4 Sector is the region between the chord and its corresponding arc. Is it true or false?
- 1.1.5 सिद्ध कीजिए कि किसी समचतुर्भुज की किसी भुजा को व्यास मानकर खींचा गया वृत्त उसके विकर्णों के प्रतिच्छेद बिन्दु से होकर जाता है।
- 1.1.6 If diagonals of a cyclic quadrilateral are diameters of the circle through the vertices of the quadrilateral, prove that it is a rectangle.
- 1.1.7 ABC and ADC are two right triangles with common hypotenuse AC. Prove that ∠CAD = ∠CBD.
- 1.1.1 Hindi and English Medium Solutions
- 1.1 Class 9 Maths Chapter 10 Circles – वृत Solutions
NCERT Solutions for Class 9 Maths Chapter 10
NCERT Solutions and CBSE Offline Apps of other subjects are also available free to use or download. Solutions are prepared for CBSE & UP Board students appearing in 2019-20 CBSE Exams and following the updated NCERT Books.
Go Back to Class 9 Maths Main Page
Class 9 Maths Chapter 10 Circles – वृत Solutions
Hindi and English Medium Solutions
- Class 9 Maths Chapter 10 Exercise 10.1 Solutions
- 9 Maths Exercise 10.1 Solutions
- 9 गणित प्रश्नावली 10.1 के हल
- Download Exercise 10.1 in PDF
- Class 9 Maths Chapter 10 Exercise 10.2 Solutions
- 9 Maths Exercise 10.2 Solutions
- 9 गणित प्रश्नावली 10.2 के हल
- Download Exercise 10.2 in PDF
- Class 9 Maths Chapter 10 Exercise 10.3 Solutions
- 9 Maths Exercise 10.3 Solutions
- 9 गणित प्रश्नावली 10.3 के हल
- Download Exercise 10.3 in PDF
- Class 9 Maths Chapter 10 Exercise 10.4 Solutions
- 9 Maths Exercise 10.4 Solutions
- 9 गणित प्रश्नावली 10.4 के हल
- Download Exercise 10.4 in PDF
- Class 9 Maths Chapter 10 Exercise 10.5 Solutions
- 9 Maths Exercise 10.5 Solutions
- 9 गणित प्रश्नावली 10.5 के हल
- Download Exercise 1.5 in PDF
- Class 9 Maths Chapter 1 Exercise 10.6 Solutions
- 9 Maths Exercise 10.6 Solutions
- 9 गणित प्रश्नावली 10.6 के हल
- Download Exercise 10.6 in PDF
- NCERT Books for Class 9 All Subjects
- NCERT Exemplar Problems Solutions
- Study Material for 2019-20 – English Medium
- Study Material for 2019-20 – Hindi Medium
9 Maths Exercise 10.1 Solutions
NCERT Solutions for Class 9 Maths Chapter 10 Circles Exercise 10.1 are given below. For other questions please visit to Exercise 10.2 or Exercise 10.3 or Exercise 10.4 or Exercise 10.5 or Exercise 10.6 or go for हिंदी मीडियम Solutions. Visit to Class 9 Maths main page or Top of the page.
9 Maths Exercise 10.2 Solutions
9 Maths Chapter 10 Exercise 10.2 is given below. For other questions please visit to Exercise 10.1 or Exercise 10.3 or Exercise 10.4 or Exercise 10.5 or Exercise 10.6 or go for हिंदी मीडियम Solutions. Visit to Class 9 Maths main page or Top of the page.
9 Maths Exercise 10.3 Solutions
9 Maths Chapter 10 Circles Exercise 10.3 is given below. For other questions please visit to Exercise 10.1 or Exercise 10.2 or Exercise 10.4 or Exercise 10.5 or Exercise 10.6 or go for हिंदी मीडियम Solutions. Visit to Class 9 Maths main page or Top of the page.
9 Maths Exercise 10.4 Solutions
Class 9 Maths Chapter 10 Circles Exercise 10.4 is given below. For other questions please visit to Exercise 10.1 or Exercise 10.2 or Exercise 10.3 or Exercise 10.5 or Exercise 10.6 or go for हिंदी मीडियम Solutions. Visit to Class 9 Maths main page or Top of the page.
9 Maths Exercise 10.5 Solutions
Questions of 9 Maths Chapter 10 Circles Exercise 10.5 are given below. For other questions please visit to Exercise 10.1 or Exercise 10.2 or Exercise 10.3 or Exercise 10.4 or Exercise 10.6 or go for हिंदी मीडियम Solutions. Visit to Class 9 Maths main page or Top of the page.
9 Maths Exercise 10.6 Solutions
Solutions of 9 Maths Chapter 10 Circles Exercise 10.6 are given below. For other questions please visit to Exercise 10.1 or Exercise 10.2 or Exercise 10.3 or Exercise 10.4 or Exercise 10.5 or go for हिंदी मीडियम Solutions. Visit to Class 9 Maths main page or Top of the page.
9 गणित प्रश्नावली 10.1 के हल
NCERT Sols 9 Maths Chapter 10 Circles Exercise 10.1 in Hindi are given below. For other questions please visit to प्रश्नावली 10.2 or प्रश्नावली 10.3 or प्रश्नावली 10.4 or प्रश्नावली 10.5 or प्रश्नावली 10.6 or go for English Medium Solutions. Visit to Class 9 Maths main page or Top of the page.
9 गणित प्रश्नावली 10.2 के हल
9 Maths Chapter 10 Circles Exercise 10.2 in Hindi is given below. For other questions please visit to प्रश्नावली 10.1 or प्रश्नावली 10.3 or प्रश्नावली 10.4 or प्रश्नावली 10.5 or प्रश्नावली 10.6 or go for English Medium Solutions. Visit to Class 9 Maths main page or Top of the page.
9 गणित प्रश्नावली 10.3 के हल
NCERT Sols 9 Maths Chapter 10 Exercise 10.3 in Hindi are given below. For other questions please visit to प्रश्नावली 10.1 or प्रश्नावली 10.2 or प्रश्नावली 10.4 or प्रश्नावली 10.5 or प्रश्नावली 10.6 or go for English Medium Solutions. Visit to Class 9 Maths main page or Top of the page.
9 गणित प्रश्नावली 10.4 के हल
Class 9 Maths Chapter 10 Circles Exercise 10.4 in Hindi is given below. For other questions please visit to प्रश्नावली 10.1 or प्रश्नावली 10.2 or प्रश्नावली 10.3 or प्रश्नावली 10.5 or प्रश्नावली 10.6 or go for English Medium Solutions. Visit to Class 9 Maths main page or Top of the page.
9 गणित प्रश्नावली 10.5 के हल
NCERT solutions 9 Maths Chapter 10 Circles Exercise 10.5 in Hindi are given below. For other questions please visit to प्रश्नावली 10.1 or प्रश्नावली 10.2 or प्रश्नावली 10.3 or प्रश्नावली 10.4 or प्रश्नावली 10.6 or go for English Medium Solutions. Visit to Class 9 Maths main page or Top of the page.
9 गणित प्रश्नावली 10.6 के हल
9 Maths Chapter 10 Exercise 10.6 in Hindi are given below. For other questions please visit to प्रश्नावली 10.1 or प्रश्नावली 10.2 or प्रश्नावली 10.3 or प्रश्नावली 10.4 or प्रश्नावली 10.5 or go for English Medium Solutions. Visit to Class 9 Maths main page or Top of the page.
Visit to Class 9 Maths main page or Top of the page
Important Terms and Theorems on
Circles – वृत
- Circle: A circle is the collection of all points in a plane, which are at a fixed distance from a fixed point in the plane.
- Diameter: It is the longest chord of the circle.
- Circumference: The length of complete circle is called its circumference.
- Arc: A piece of circle between two point is called arc.
- Segment: The region between a chord and either of its arcs is called a segment of circular region.
- Properties related to CIRCLE
- Equal chords of a circle subtend equal angles at the centre.
- If the angles subtended by two chords of a circle at the centre are equal, the chords are also equal.
- The perpendicular from the centre of a circle to a chord bisects the chord.
- The line drawn through the centre of a circle to bisect a chord is perpendicular to the chord.
- There is one and only one circle passing through three non-collinear points.
Theorems on Circles for class 9
- Equal chords of a circle are equidistant from the centre and cords equidistant from the centre of a circle are equal.
- If two arcs of a circle are congruent, then their corresponding chords are equal and conversely if two chords of a circle are equal, then their corresponding arcs are congruent.
- Congruent arcs of a circle subtend equal angles at the centre.
- The angle subtended by an arc at the centre is double the angle subtended by it at any point on the remaining part of the circle.
- Angles in the same segment of a circle are equal.
- Angle in a semi-circle is a right angle.
- The sum of either pair of opposite angles of a cyclic quadrilateral is 180 and if the sum of a pair of opposite angles of a quadrilateral is 180, then the quadrilateral is cyclic.
Table of Contents
- 1 Fill in the blank: The centre of a circle lies in _____________ of the circle.
- 2 याद कीजिए कि दो वृत्त सर्वांगसम होते हैं, यदि उनकी त्रिज्याएँ बराबर हों। सिद्ध कीजिए कि सर्वांगसम वृत्तों की बराबर त्रिज्याएँ उनके केन्द्रों पर बराबर कोण अंतरित करती हैं।
- 3 Sector is the region between the chord and its corresponding arc. Is it true or false?
- 4 सिद्ध कीजिए कि किसी समचतुर्भुज की किसी भुजा को व्यास मानकर खींचा गया वृत्त उसके विकर्णों के प्रतिच्छेद बिन्दु से होकर जाता है।
- 5 If diagonals of a cyclic quadrilateral are diameters of the circle through the vertices of the quadrilateral, prove that it is a rectangle.
- 6 ABC and ADC are two right triangles with common hypotenuse AC. Prove that ∠CAD = ∠CBD.
Fill in the blank: The centre of a circle lies in _____________ of the circle.
याद कीजिए कि दो वृत्त सर्वांगसम होते हैं, यदि उनकी त्रिज्याएँ बराबर हों। सिद्ध कीजिए कि सर्वांगसम वृत्तों की बराबर त्रिज्याएँ उनके केन्द्रों पर बराबर कोण अंतरित करती हैं।
सिद्ध करना है: ∠BAC = ∠QPR
उपपत्ति: ABC और PQR में,
BC = QR [∵ दिया है] AB = PQ [∵ सर्वांगसम वृत्तों की त्रिज्याएँ] AC = PR [∵ सर्वांगसम वृत्तों की त्रिज्याएँ] अतः, ABC ≅ PQR [∵SSS सर्वांगसमता नियम] ∠BAC = ∠QPR [∵ सर्वांगसम त्रिभुज के संगत भाग बराबर होते हैं]
Sector is the region between the chord and its corresponding arc. Is it true or false?
False.
Because, between chord and arc a segment is formed. Sector is the region which is formed between radii and arc.
सिद्ध कीजिए कि किसी समचतुर्भुज की किसी भुजा को व्यास मानकर खींचा गया वृत्त उसके विकर्णों के प्रतिच्छेद बिन्दु से होकर जाता है।
सिद्ध करना है: AB को व्यास मानकर खींचा गया वृत्त विकर्णों के प्रतिच्छेद बिन्दु O से होकर जाता है।
उपपत्ति: ABCD एक समचतुर्भु है। अतः, ∠AOC = 90°
[∵ समचतुर्भुज के विकर्ण एक दूसरे को लम्ब समद्विभाजित करते हैं] AB को व्यास मानकर खींचा गया वृत्त बिन्दु O से हो कर जाएगा।
[∵ अर्धवृत्त में बना कोण समकोण होता है] अतः, समचतुर्भुज की किसी भुजा को व्यास मानकर खींचा गया वृत्त उसके विकर्णों के प्रतिच्छेद बिन्दु से होकर जाता है।
If diagonals of a cyclic quadrilateral are diameters of the circle through the vertices of the quadrilateral, prove that it is a rectangle.
Hence, ∠ADC = 90° and ∠ABC = 90° … (1)
[∵ Angle in a semicircle is a right angle.]
Similarly, BD is diameter of circle.
Hence, ∠BAD = 90° and ∠BCD = 90° … (2)
[∵ Angle in a semicircle is a right angle.]
From the equation (1) and (2),
∠ADC =∠ABC = ∠BAD = ∠BCD = 90°
Hence, ABCD is a rectangle.
ABC and ADC are two right triangles with common hypotenuse AC. Prove that ∠CAD = ∠CBD.
To prove: ∠CAD = ∠CBD.
Proof: Triangle ABC and ADC are on common base BC and ∠BAC = ∠BDC.
Hence, points A, B, C and D lie on the same circle.
[∵ If a line segment joining two points subtends equal angles at two other points lying on the same side of the line containing the line segment, the four points lie on a circle.] Therefore,
∠CAD = ∠CBD
[∵ Angles in the same segments are equal]
good plateform for teachers and students
thanks