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The diameter of a circle is AB. Point C is on the circumference. What is the measure of the ∠ACB? Explain your reasoning.
AB is the diameter of the circle and C is a point on its circumference. According to the theorem, the angle subtended by a diameter at any point on the circle is 90°. Here, the diameter AB subtends ∠ACB at point C. Therefore, ∠ACB = 90°. Hence, the measure of ∠ACB is 90°. For more NCERT SolutRead more
AB is the diameter of the circle and C is a point on its circumference. According to the theorem, the angle subtended by a diameter at any point on the circle is 90°. Here, the diameter AB subtends ∠ACB at point C. Therefore,
∠ACB = 90°.
Hence, the measure of ∠ACB is 90°.
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 lessABCD is a cyclic quadrilateral inscribed in a circle. If ∠A measures 75°, what is the measure of ∠C? If ∠B measures 110°, what is the measure of ∠D?
ABCD is a cyclic quadrilateral. According to the property of a cyclic quadrilateral, the sum of each pair of opposite angles is 180°. For angles A and C: ∠C = 180° - 75° = 105° For angles B and D: ∠D = 180° - 110° = 70° Therefore, ∠C = 105° and ∠D = 70°. For more NCERT Solutions for Class 9 MRead more
ABCD is a cyclic quadrilateral. According to the property of a cyclic quadrilateral, the sum of each pair of opposite angles is 180°.
For angles A and C:
∠C = 180° – 75° = 105°
For angles B and D:
∠D = 180° – 110° = 70°
Therefore, ∠C = 105° and ∠D = 70°.
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 lessQuadrilateral PQRS is inscribed in a circle. If ∠P = (2x + 10)° and ∠R = (3x – 20)°, find the value of x and the measures of ∠P and ∠R.
PQRS is a cyclic quadrilateral, so its opposite angles P and R are supplementary. Therefore, (2x + 10) + (3x - 20) = 180 5x - 10 = 180 5x = 190 x = 38 Now, ∠P = 2(38) + 10 = 86° ∠R = 3(38) - 20 = 94° Hence, x = 38, ∠P = 86° and ∠R = 94°. For more NCERT Solutions for Class 9 Maths Ganita ManjaRead more
PQRS is a cyclic quadrilateral, so its opposite angles P and R are supplementary.
Therefore,
(2x + 10) + (3x – 20) = 180
5x – 10 = 180
5x = 190
x = 38
Now,
∠P = 2(38) + 10 = 86°
∠R = 3(38) – 20 = 94°
Hence, x = 38, ∠P = 86° and ∠R = 94°.
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 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