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What is atmosphere? Explain its composition with the help of a pie diagram.
The atmosphere is the layer of gases surrounding the Earth, held by gravity, and vital for the survival of living beings. It is composed mainly of nitrogen (78%) and oxygen (21%), along with small amounts of argon (0.93%), carbon dioxide (0.04%), and other gases (0.03%) including water vapour and duRead more
The atmosphere is the layer of gases surrounding the Earth, held by gravity, and vital for the survival of living beings. It is composed mainly of nitrogen (78%) and oxygen (21%), along with small amounts of argon (0.93%), carbon dioxide (0.04%), and other gases (0.03%) including water vapour and dust particles. Nitrogen and oxygen together make up about 99% of the atmosphere, while the remaining gases, though present in small quantities, play important roles such as trapping heat (carbon dioxide) and supporting cloud formation and precipitation (water vapour). The composition also varies with altitude.
Learn with detailed, step-by-step solutions: https://www.tiwariacademy.com/ncert-solutions/class-9/social-science/chapter-3/
See lessShow that the triangle formed by a chord and the centre of the circle is isosceles.
Let AB be a chord and O be the centre of the circle. Join OA and OB. Since OA and OB are radii of the same circle, they are equal in length. A triangle having two equal sides is an isosceles triangle. Therefore, the triangle formed by the chord and the centre of the circle is an isosceles triangle.Read more
Let AB be a chord and O be the centre of the circle. Join OA and OB. Since OA and OB are radii of the same circle, they are equal in length. A triangle having two equal sides is an isosceles triangle. Therefore, the triangle formed by the chord and the centre of the circle is an isosceles triangle.
For more NCERT Solutions for Class 9 Maths Ganita Manjari Chapter 5 I’m Up and Down and Round and Round (2026-27):
https://www.tiwariacademy.com/ncert-solutions/class-9/maths/ganita-manjari-chapter-5/
See lessShow that if two such isosceles triangles (occurring in the previous question) have equal base length, they are congruent to each other.
Consider two triangles formed by equal chords and the centre of the same circle. Each triangle has two sides equal to the radii of the circle, and the given base lengths are also equal. Thus, all three corresponding sides of the triangles are equal. Therefore, the triangles are congruent by the SSSRead more
Consider two triangles formed by equal chords and the centre of the same circle. Each triangle has two sides equal to the radii of the circle, and the given base lengths are also equal. Thus, all three corresponding sides of the triangles are equal. Therefore, the triangles are congruent by the SSS Congruence Criterion.
For more NCERT Solutions for Class 9 Maths Ganita Manjari Chapter 5 I’m Up and Down and Round and Round (2026-27):
https://www.tiwariacademy.com/ncert-solutions/class-9/maths/ganita-manjari-chapter-5/
See lessCan you explain why the converse to Theorem 4 is true, i.e., why does the perpendicular from the centre of a circle to a chord of the circle bisect the chord? (Hint: Use Fig. 5.12. You are told that ∠CMA = ∠CMB = 90°. You need to show that AM = BM.)
Let CM be perpendicular to chord AB. The triangles CMA and CMB are right triangles. Their hypotenuses, CA and CB, are equal because they are radii of the same circle, and CM is common. Hence, the triangles are congruent by the RHS Congruence Criterion. Therefore, AM = BM, proving that the perpendicuRead more
Let CM be perpendicular to chord AB. The triangles CMA and CMB are right triangles. Their hypotenuses, CA and CB, are equal because they are radii of the same circle, and CM is common. Hence, the triangles are congruent by the RHS Congruence Criterion. Therefore, AM = BM, proving that the perpendicular from the centre bisects the chord.
For more NCERT Solutions for Class 9 Maths Ganita Manjari Chapter 5 I’m Up and Down and Round and Round (2026-27):
https://www.tiwariacademy.com/ncert-solutions/class-9/maths/ganita-manjari-chapter-5/
See lessAn isosceles triangle ABC is inscribed in a circle, with AB = AC. Show that the altitude from A to BC passes through the centre of the circle.
Since AB = AC, triangle ABC is isosceles. The altitude drawn from A to BC also bisects BC. As BC is a chord of the circumcircle, its perpendicular bisector always passes through the centre of the circle. Therefore, the altitude from A to BC passes through the centre of the circle. For more NCRead more
Since AB = AC, triangle ABC is isosceles. The altitude drawn from A to BC also bisects BC. As BC is a chord of the circumcircle, its perpendicular bisector always passes through the centre of the circle. Therefore, the altitude from A to BC passes through the centre of the circle.
For more NCERT Solutions for Class 9 Maths Ganita Manjari Chapter 5 I’m Up and Down and Round and Round (2026-27):
https://www.tiwariacademy.com/ncert-solutions/class-9/maths/ganita-manjari-chapter-5/
See less