Q1
The angle at the centre is:
Atwice the angle at the circumference (for the same arc)
Bhalf the angle at the circumference
Cequal to the angle at the circumference
Dunrelated to the circumference angle
CBSEClass 9 (CBSE)MathematicsCh 9 · Topic 2
Angle Subtended by an Arc
Learning the relationship between angles subtended by an arc at the centre and circumference.
Core concept
A direct and useful consequence of this theorem is that angles in the same segment of a circle (subtended by the same arc, on the same side) are always equal to each other, since they are all exactly half of the same fixed central angle. Another important consequence: an angle inscribed in a semicircle (subtended by the diameter) is always exactly 90°, since the central angle for a diameter is 180° (a straight line), and half of 180° is 90°.
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• The angle at the centre is twice the angle at the circumference, subtended by the same arc.
• Angles in the same segment (subtended by the same arc) are equal to each other.
• An angle inscribed in a semicircle (subtended by the diameter) is always 90°.
• This theorem connects central angles and circumference (inscribed) angles.