Class 9 · Chapter 9
Circles
Chords and arcs; angles subtended by chords at the centre and circumference; cyclic quadrilaterals.
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Detailed theory
Chord: segment joining two points on a circle. Diameter: longest chord (through the centre). Arc: portion of the circle between two points. Sector: region between two radii. Segment: region between a chord and an arc. Cyclic polygon: has all vertices on a circle.
Key concepts & formulas
01
Equal chords subtend equal angles at the centre.
02
Perpendicular from centre to chord bisects the chord.
03
Angle subtended by an arc at the centre is twice the angle at the circumference.
04
Angles in the same segment are equal.
05
Opposite angles of a cyclic quadrilateral sum to .
06
Angle in a semicircle is .