Angle properties of a circle refer to the specific geometric rules governing the relationship between angles formed by points, arcs, chords, and tangents within a circle.
Angles subtended by an arc or a chord
The figure below helps us study the angles subtended by an arc or a chord in the same segment at the circumference.
angle a, b and c are equal. The three angles are subtended at the circumference of the circle by the chord AC. All the three angles are in the same segment AFEDC we conclude that:
Angles subtended by the same arc or chord at the circumference, in the same arc are equal.
Angle subtended by equal arcs
Equal arcs are enclosed by equal chords. If chords of a circle are equal, then they are subtends equal angles at the circumference.
In the figure below chord AC and ZY are equal. Therefore angle ABC and angle ZXY are equal.
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