∠MOP is the angle subtended by arc MP at the centre, while ∠MNP is subtended by the same arc at the circumference. Therefore, the central angle is twice the angle at the circumference.
A quadrilateral MNOP is inscribed in a circle. If MN is a diameter, what can you say about ∠MOP and ∠MNP? Explain your reasoning.
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Since MNOP is inscribed in a circle, both ∠MOP and ∠MNP subtend the same arc MP. ∠MOP is formed at the centre of the circle, whereas ∠MNP is formed at a point on the circumference. According to the theorem, the angle subtended by an arc at the centre is twice the angle subtended by the same arc at any point on the remaining circle.
Therefore,
∠MOP = 2∠MNP.
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/