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In a circle with centre O, the central angle AOB is 60°. If the radius of the circle is 12 cm, what is the length of the chord AB?
OA and OB are radii of the circle, so OA = OB = 12 cm. Therefore, triangle AOB is isosceles. Since ∠AOB = 60°, the remaining two angles together are 120° and each is 60°. Hence, triangle AOB is an equilateral triangle. All its sides are equal. Therefore, AB = OA = OB = 12 cm. So, the length of chordRead more
OA and OB are radii of the circle, so OA = OB = 12 cm. Therefore, triangle AOB is isosceles. Since ∠AOB = 60°, the remaining two angles together are 120° and each is 60°. Hence, triangle AOB is an equilateral triangle. All its sides are equal. Therefore, AB = OA = OB = 12 cm. So, the length of chord AB is 12 cm.
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 lessLet A and B be two points on a circle with centre O. (i) Are there points X, Y on the circle, on the same side of AB, such that ∠AXB is different from ∠AYB?
No. There cannot be such points X and Y on the same side of AB for which ∠AXB is different from ∠AYB. According to Theorem 9, an arc subtends the same angle at every point on the remaining part of the circle. Therefore, when X and Y lie on the same side of AB, both angles subtend the same chord AB aRead more
No. There cannot be such points X and Y on the same side of AB for which ∠AXB is different from ∠AYB. According to Theorem 9, an arc subtends the same angle at every point on the remaining part of the circle. Therefore, when X and Y lie on the same side of AB, both angles subtend the same chord AB and are equal.
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(ii) Is it true that if ∠AXB = ∠AYB, then X and Y lie on the same side of the circle?
Yes. If ∠AXB = ∠AYB and X and Y lie on the same side of AB, then both points lie on the same segment of the circle. The angle subtended by a chord at points on the same segment is equal. Hence, equal angles are obtained at X and Y. This follows directly from the property that an arc subtends equal aRead more
Yes. If ∠AXB = ∠AYB and X and Y lie on the same side of AB, then both points lie on the same segment of the circle. The angle subtended by a chord at points on the same segment is equal. Hence, equal angles are obtained at X and Y. This follows directly from the property that an arc subtends equal angles at points on the remaining part 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 lessIf ∠AXB = ∠AYB and X and Y do not lie on the circle, does the circle through A, B and X also pass through Y?
Yes. Since ∠AXB = ∠AYB, the line segment AB subtends equal angles at X and Y. If X and Y are on the same side of AB, Theorem 10 states that the four points A, B, X and Y lie on a circle. Therefore, the circle passing through A, B and X will also pass through Y. Thus, A, B, X and Y are concyclic.Read more
Yes. Since ∠AXB = ∠AYB, the line segment AB subtends equal angles at X and Y. If X and Y are on the same side of AB, Theorem 10 states that the four points A, B, X and Y lie on a circle. Therefore, the circle passing through A, B and X will also pass through Y. Thus, A, B, X and Y are concyclic.
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 lessFind x in Fig. 5.26.
Since A, B, C and D lie on the same circle, ABCD is a cyclic quadrilateral. In a cyclic quadrilateral, the sum of two opposite angles is 180°. Here, ∠D = 100° and ∠B = x. Therefore, x + 100° = 180° x = 180° - 100° x = 80° Hence, the value of x is 80°. For more NCERT Solutions for Class 9 MathRead more
Since A, B, C and D lie on the same circle, ABCD is a cyclic quadrilateral. In a cyclic quadrilateral, the sum of two opposite angles is 180°.
Here, ∠D = 100° and ∠B = x.
Therefore,
x + 100° = 180°
x = 180° – 100°
x = 80°
Hence, the value of x is 80°.
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