Q1
What is the relationship between central and inscribed angles on the same arc?
ACentral angle is twice the inscribed angle
BThey are always equal
CInscribed angle is twice the central angle
DNo relationship exists
ICSEClass 10 (ICSE)MathematicsCh 17 · Topic 2
Practice and Revision - Circles
Let us practise and revise what we learned about circles. Circle theorems describe relationships between angles, chords, and arcs, essential
Core concept
The angle subtended by an arc at the centre is twice the angle subtended by the same arc at any point on the remaining part of the circle.
How it works
Angles in the same segment of a circle, subtended by the same arc, are equal to each other.
Why it matters
The angle in a semicircle is always a right angle (90°), a special case of the angle-arc relationship.
Key detail
Opposite angles in a cyclic quadrilateral (one inscribed in a circle) are supplementary, adding up to 180°.
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Quick notes
• Central angle = 2 × inscribed angle (same arc).
• Angles in the same segment are equal.
• Angle in a semicircle is always 90°.
• This is a special case of the angle-arc rule.
• Cyclic quadrilateral opposite angles sum to 180°.
• These are key circle theorems.
• They help solve circle geometry problems.
• Practice builds theorem application skills.