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(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 lessIn a circle, a chord is 5 cm away from the centre. If the radius of the circle is 13 cm, what is the length of the chord?
Let the perpendicular distance from the centre to the chord be 5 cm and the radius be 13 cm. The perpendicular from the centre to a chord bisects the chord. Thus, we get a right triangle with hypotenuse 13 cm and one side 5 cm. Half chord = √(13² - 5²) = √144 = 12 cm Therefore, length of the chord =Read more
Let the perpendicular distance from the centre to the chord be 5 cm and the radius be 13 cm. The perpendicular from the centre to a chord bisects the chord. Thus, we get a right triangle with hypotenuse 13 cm and one side 5 cm.
Half chord = √(13² – 5²) = √144 = 12 cm
Therefore, length of the chord = 2 × 12 = 24 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 lessSolve the previous question using the Baudhāyana–Pythagoras theorem.
Draw perpendiculars from the centre to both chords. The radii are equal, and the perpendicular distances are also equal. Using the Baudhāyana–Pythagoras Theorem, the half-lengths of both chords are equal. Doubling these equal half-chords gives equal full chord lengths. Therefore, the two chords areRead more
Draw perpendiculars from the centre to both chords. The radii are equal, and the perpendicular distances are also equal. Using the Baudhāyana–Pythagoras Theorem, the half-lengths of both chords are equal. Doubling these equal half-chords gives equal full chord lengths. Therefore, the two chords are equal, proving that AB = GF.
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