plzz give a short summary of Circle class 9
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Step-by-step explanation:
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in circles chapter there are many theorems
Theorem 1: Any two equal chords of a circle subtend equal angles at the centre.
Theorem 2: If the angles made by the chords of a circle at the centre are equal, then the chords must be equal.
Theorem 3: If we draw a perpendicular from the centre of a circle to any chord then it bisects the chord.
Theorem 4: The line which is drawn from the centre of a circle to bisect a chord must be perpendicular to the chord.
Circles
Any closed shape with all points connected at equidistance from centre forms a Circle.
Any point which is at equidistance from anywhere from its boundary is known as the Centre of the Circle.
Radius is a Latin word which means ‘ray' but in the circle it is the line segment from the centre of the Circle to its edge. So any line starting or ending at the centre of the circle and joining anywhere on the border on the circle is known as the Radius of Circle.
Interior and Exterior of a Circle
In a flat surface, the interior of a circle is the line whose distance from the centre is less than the radius.
The exterior of a circle is the line in the plane whose distance from the centre is larger than the radius.
Terms related to circle
Chord: Any straight line segment that’s both endpoints falls on the boundary of the circle is known as Chord. In Latin, it means ‘bowstring’.
Diameter: Any straight line segment or Chord which passes through the centre of the Circle and its endpoints connects on the boundary of the Circle is known as the Diameter of Circle. So in a circle Diameter is the longest chord possible in a circle.
Arc: Any smooth curve joining two points is known as Arc. So in Circle, we can have two possible Arcs, the bigger one is known as Major Arc and the smaller one is known as Minor Arc.
Circumference: It is the length of the circle if we open and straightened out to make a line segment.
Segment and Sector of the Circle
A segment of the circle is the region between either of its arcs and a chord. It could be a major or minor segment.
Sector of the circle is the area covered by an arc and two radii joining the centre of the circle. It could be the major or minor sector.