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NCERT Solutions for Class 9 Maths, Free NCERT Solutions Nov 03, �� In this section, NCERT Solutions of Chapter 10 Maths Class 9 defines circle as, The collection of every point in a plane, which is at a fixed distance from a fixed point in the plane, is known as a circle. The entire circle is divided into two - inside of the circle is the interior region and outside of the circle is the exterior region.
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If diagonals of a cyclic quadrilateral are diameters of the circle through the vertices of the quadrilateral, prove that it is a rectangle. If the non � parallel sides of a trapezium are equal, prove that it is cyclic. Two circles intersect at two points B and C. Solution: Since, angles in the same segment of a circle are equal.

If circles are drawn taking two sides of a triangle as diameters, prove that the point of intersection of these circles lie on the third side.

They intersect at a point D, other than A. Let us join A and D. Thus, D lies on BC. Case � I: If both the triangles are in the same semi-circle. Join BD. DC is a chord. Case � II : If both the triangles are not in the same semi-circle. Prove that a cyclic parallelogram is a rectangle. Since, ABCD is a cyclic quadrilateral. Thus, ABCD is a rectangle. Prove that the line of centres of two intersecting circles subtends equal angles at the two points of intersection.

Two chords AB and CD of lengths 5 cm and 11 cm, respectively of a circle are parallel to each other and are on opposite sides of its centre. If the distance between AB and CD is 6 cm, find the radius of the circle. Solution: We have a circle with centre O. Let r cm be the radius of the circle. The lengths of two parallel chords of a circle are 6 cm and 8 cm. If the smaller chord is at distance 4 cm from the centre, what is the distance of the other chord from the centre? Parallel chords AB and CD are such that the smaller chord is 4 cm away from the centre.

Let the vertex of an angle ABC be located outside a circle and let the sides of the angle intersect equal chords AD and CE with the circle. Proof: An exterior angle of a triangle is equal to the sum of interior opposite angles. Prove that the circle drawn with any side of a rhombus as diameter, passes through the point of intersection of its diagonals.

Chapter 1 - Number System. Chapter 2 - Polynomials. Chapter 3 - Coordinate Geometry. Chapter 4 - Linear Equations in Two Variables. Chapter 6 - Lines and Angles.

Chapter 7 - Triangles. Chapter 8 - Quadrilaterals. Chapter 9 - Areas of Parallelogram and Triangles. Chapter 10 - Circles. Chapter 11 - Constructions. Chapter 12 - Herons formula. Chapter 13 - Surface area and Volumes. Chapter 14 - Statistics. Chapter 15 - Probability. This helps the students to get rid of bothering about internet connections. This can be stored as a soft copy as well as a hard copy for Future. Well-experienced mathematics teachers prepared these materials as per the latest curriculum.

Exercise Furthermore, you will get to learn about finding the area of triangles, quadrilaterals, and various types of polygons. Along with the, is there is also knowledge of formula for the plane figures given in the chapter. Every one of you has already studied mensuration in previous standards. Thus, you must be aware of surface areas and this chapter is on that. Along with this, this chapter also has a volume of cubes, cylinders, cuboids, cones, hemispheres, and spheres.

Also, in this chapter, you will get to know about the conversion of one figure into another, and comparing volumes of two figures. In this chapter, you will get the knowledge about the descriptive statistics and the collection of data based on different aspects of life.

This is useful for interpretation and stating the inferences from the data. This chapter gives the basic knowledge of the collection of data as the data is available in raw form. As you move forward and study 5 exercises you will learn about presenting data in tabular form by keeping them together in regular intervals, polygon, histogram, or bar graph drawing. You will also get to the topics like mean, median, and mode and finding the central tendency with the raw data.

Probability in this book is based on the observation approach or finding the frequency. Questions in this chapter are very intuitive as they are based on daily life or day to day situations. For example, incidents like throwing dice, coin tossing, the probability for a deck of cards and simple events.

If you are curious this chapter can be very interesting for you to learn and understand. There may be a few times where you feel you are stuck and not getting the desired solutions.

NCERT has few questions but has great importance in papers. Access the direct links available on our page and download them for free of cost. Try practicing as much as you can and revise the complete syllabus of Class 9 Maths for the exams to score well. If you have any doubt regarding this article or class 9 Maths NCERT Solutions, leave your comments in the comment section below and we will get back to you as soon as possible.

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