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NCERT Solutions for Class 9 Maths Chapter 10 Circles (Ex ) Exercise

Circle: A 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 Class 9 Maths Ch 10 Ex 10.5 Inc the circle. Circumference: The length of complete circle is called its circumference. Arc: A piece of circle between two class 9 maths ch 10 ex 10.5 inc is called arc.

Segment: The region between a Class 9 Maths Ch 10 Ex 10.5 Inc 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 the angles subtended by two chords of a circle at the centre are equal, the 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 Maths 10.5 10 Ex Class Inc 9 Ch 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 Class 9 Maths Ch 10 Ex 10.5 Inc of circles and giving proper examples. In few questions some axioms of circles are also used as theorems. Study Material for What Class 9 Maths Ch 10 Ex 10.5 Inc do understand by a circle? What are the Class 9 Maths Ch 10 Ex 10.5 Inc components of a circle? What are the main Properties related to a circle?

Important Theorems on Circles Class 9 Maths Chapter 10 Equal chords of a circle are equidistant Ex Ch Maths Class 9 Inc 10 10.5 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 at 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 same segment of a circle are equal. Class 9 maths ch 10 Class 9 Maths Ch 10 Ex 10.5 Inc ex 10.5 inc in a semi-circle is a right angle. The sum of Class 9 Maths Ch 10 Ex 10.5 Inc either pair of opposite angles of a cyclic quadrilateral is and if the sum of a pair of opposite angles of Class 9 Maths Ch 10 Ex 10.5 Free a Class 9 Maths Ch 10 Ex 10.5 Inc quadrilateral isthen the quadrilateral is cyclic. The centre Class 9 Maths Ch 10 Ex 10.5 Inc of a circle lies in interior of Class 9 Maths Ch 10 Ex 10.5 Inc the circle.

Class 9 maths ch 10 ex 10.5 inc circle has only finite number of equal chords. True or False? Because, Class 9 Maths Ch 10 Ex 10.5 Inc there are infinite number of equal Ex Class Inc 10 Maths Ch 9 10.5 chords in a circle. Sector Ch 11 Of Maths Class 10 Inch 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 the vertices of the quadrilateral, prove that it is a rectangle.

AC is diameter of circle. Hence, points A, B, C and D lie on the same Class 9 Maths Ch 10 Ex 10.5 Inc circle. Constructions �.

Give a construction to find its centre. If diagonals of a cyclic quadrilateral are diameters of the circle through the vertices of the quadrilateral, prove that it is a rectangle. Ths students need to follow the property that the angles in the same segment of a circle are Class 9 Maths Ch 10 Ex 10.5 Inc equal. This question follows the same approach as the previous one - that the angles in the same segment are equal. If the smaller chord is at distance 4 cm Class 9 Maths Ch 10 Ex 10.5 Inc from the centre, what is the distance of the other chord from the centre? Suppose it cuts circumcirde at P. Solution: Given : Two circles with the common centre O.

Thus:

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