Students can go through AP Board 9th Class Maths Notes Chapter 12 Circles to understand and remember the concepts easily.
AP State Board Syllabus 9th Class Maths Notes Chapter 12 Circles
→ A collection of all points in a plane which are at a fixed distance from a fixed point in the sapie plane is called a circle. The fixed point is called the centre and the fixed distance is called the radius of the circle.
→ A line segment joining any two points on the circle is called a chord.
→ The longest of all chords which passes through the centre is called a diameter.
→ Circles with same radii are called congruent circles.
→ Circles with same centre and different radii are called concentric circles.
→ Diameter of a circle divides it into two semi-circles.
→ The part between any two points on the circle is called an arc.
→ The area enclosed by a chord and an arc is called a segment. If the arc is a minor arc then it is called the minor segment and if the arc is major arc then it is called the major segment.
→ The area enclosed by an arc and the two radii joining the end points of the arc with centre is called a sector.
→ Equal chords of a circle subtend equal angles at the centre.
→ Angles in the same segment are equal.
→ An angle in a semi circle is a right angle.
→ If the angles subtended by two chords at the centre are equal, then the chords are congruent.
→ The perpendicular from the centre of a circle to a chord bisects the chords. The converse is also true.
→ There is exactly one circle that passes through three non-collinear points.
→ The circle passing through the three vertices of a triangle is called a circumcircle.
→ Equal chords are at equal distance from the centre of the circle, conversely chords at equidistant from the centre of the circle are equal in length.
→ Angle subtended by an arc at the centre of the circle is twice the angle subtended by it at any other point on the circle.
→ If the angle subtended by an arc at a point on the remaining part of the circle is 90°, then the arc is a semi circle.
→ If a line segment joining two points subtends same angles at two other points lying on the same side of the line segment, the four points lie on the circle.
→ The sum of pairs of opposite angles of a cyclic quadrilateral are supplementary.