TRIPURA Class 9 Maths Circles
Introduction to Circles
Circle is a closed figure on which every point is at a constant distance from a fixed point.
Chord is a line segment joining any two points on the circle and divides the circle into two parts, each part is called segment.
A continuous piece of a circle is called an Arc of the circle. The region between an arc and the two radii joining the centre to the end points of the arc is called a sector.Angle Subtended by The Chord
Equal chords of a circle subtend equal angles at the centre.
If two chords of a circle subtend equal angles at the centre, then the chords are equal.
These properties are valid in congruent circles also.
Angle subtended by a chord at the centre is double the angle subtended by it at any point on the circumference.Perpendicular From Centre to Chord
Perpendicular from centre of a circle bisects the chord.
Line segment joining the centre of a circle to the midpoint of a chord is perpendicular to the chord.
The perpendicular bisectors of two chords of a circle intersect at its centre.
There is one and only one circle which passes through 3 non-collinear points.Properties of Equal Chords
Perpendicular distance is the shortest distance of the line from a point.
Equal chords are equidistant from the centre.
Chords that are equidistant from the centre are equal in length.Cyclic Quadrilaterals
Relation between angle subtended by an arc at centre and at any point on the circumference. Angles in same segment. Properties of cyclic quadrilaterals.