Circle Properties – Class 9 Geometry
These are Some of the important properties of a circle which are very important to keep in mind for solving questions related to geometry in mathematics.
- Definition – Circle is Collection of all points in a plane which are equidistant from a fixed point on the plane.
- There is one and only one circle passing through 3 given non-collinear points.
- Equal chords of a circle subtend equal angles at the centre.
- Reverse – If the angle subtended by the chords at the centre are equal then the chords are also equal.
- The perpendicular from the centre of the circle on a chord bisects the chord.
- Reverse – Line drawn through the centre of circle to bisect a chord is perpendicular to the chord.
- Equal chords of a circle are equidistant from the centre of the circle.
- Reverse – Chords equidistant from the centre are of a circle are also equal.
- Angle in the same segment of a circle are equal
- Angle in a semicircle is a right angle.
- The angle subtended by an arc at the centre is double the angle subtended by it at any point on the remaining part of the circle.
- A quadrilateral is called cyclic if all the four vertices of it lie on a circle
- The sum of either pair of opposite angles of a cyclic quadrilateral is 180.
- Reverse – If the sum of a pair of opposite angles of a quadrilateral is 180, the quadrilateral is cyclic.
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Quadrilateral Properties & Questions
