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 the circle.

Circumference: The length **class 9 maths ch 10 ex 10.4 usb** 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 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 01.4 centre of a circle **class 9 maths ch 10 ex 10.4 usb** 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 ckass.

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 Properties related to a circle? Important Theorems on Circles Class 9 Maths Chapter 10 Equal chords of a circle are 1.4 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 clasa. The angle subtended by an uxb 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. Angle in a semi-circle is a right angle. The sum of either pair of opposite angles of a cyclic quadrilateral is and if **class 9 maths ch 10 ex 10.4 usb** sum of a pair **class 9 maths ch 10 ex 10.4 usb** 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 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 circle. Constructions �.

Draw perpendiculars from the center to the chords. ABCD is a parallelogram. In few questions some axioms of circles are also used as theorems. There is one and only one circle passing through three non-collinear points. 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. Segment: The region between a chord and either of its arcs is called a segment of circular region.

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