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Circles class 9 Notes with Solved Examples

Circle: Attqck circle is the collection of all points in a plane, which are at a fixed distance from a fixed point in the plane. Diameter: It is the longest chord of the circle. Circumference: The length of complete circle is called its circumference. Arc: A piece of circle between two point is called arc. Segment: The region between a chord and either of its arcs is called a segment of circular region.

Equal chords of a circle subtend equal angles at the centre. If attcak angles subtended by two chords of a circle at the centre are equal, byjus class 9 maths circles attack chords are also equal. The perpendicular from the centre of a circle to a chord bisects the chord.

The line drawn through the centre of a circle to bisect a chord is perpendicular to the chord. There is one and only one circle passing through three non-collinear points. Because, between chord and arc a segment is formed. Sector is the region which is formed between radii and arc.

Similarly, BD is diameter of circle. So, these solutions are applicable for all these boards. All the questions are explained well using the theorems of circles and giving proper examples.

In few questions some axioms of circles are also used as theorems. Study Material for What do understand by a circle? What are the components of a circle? What are the main Jaths related to a circle? Important Theorems on Circles Byjus class 9 maths circles attack 9 Maths Chapter 10 Equal chords of a circle are equidistant from the centre and cords equidistant from the centre of a circle are equal.

If two arcs of a circle are congruent, then their corresponding chords are equal and conversely if two chords of a circle are equal, then their corresponding arcs are congruent. Congruent arcs of a circle subtend equal angles byjus class 9 maths circles attack the centre. 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.

Angles in the cirlces segment of a circle are equal. Angle in a semi-circle is a right angle. The sum of either pair of opposite angles of a cyclic quadrilateral is and if the sum of a pair of opposite angles of a quadrilateral isthen the quadrilateral is cyclic.

The centre of a circle lies in interior of the circle. A circle has only finite number of equal chords. True or False? Because, there are infinite number of equal chords in a circle. Sector is the region between the chord and its corresponding arc. Is it true or false?

If diagonals of a cyclic quadrilateral are diameters of the circle through byjus class 9 maths circles attack vertices of the quadrilateral, cirvles that it is a rectangle. AC is diameter of circle. Hence, points A, B, C and D lie on the same circle.

Constructions �.

If the smaller chord is at distance 4 cm from the centre, what is the distance of the other chord from the centre? Proof: An exterior angle of a triangle is equal to the sum of interior opposite angles. Solution: Steps of construction : Step I : Take any three points on the given circle. Chapter 8 - Quadrilaterals. Date Added November 11, A circle drawn with Q as centre, will pass through A, B and O. A chord of a circle is equal to the radius of the circle, find the angle subtended by the chord at a point on the minor arc and also at a point on the major arc.

Make points:

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