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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 also. 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 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 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. 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 is , then the quadrilateral is cyclic.
The centre of a circle lies in interior of the circle. A circle has only finite number of equal chords. If the chord cuts the second into two halves exactly, then it is known as diameter. The longest chord in the circle is equal to the diameter. Another related term to the circle is the sector. Students can refer to class 9 chapter 10 maths to get a better understanding of this section. Students are asked to draw a card in a circle. Then extend that line to another point which joins two line segments.
It forms a triangle inside the circle. This is known as an angle subtended by a chord at a point. Based on these two theorems were explained in the PDF. If the lengths of chords are the same, then their angles are the same and vice versa. In this section, students can learn about the perpendicular drawn from the centre of the chord by making an activity.
Here also two theorems were given. The perpendicular drawn from the centre can bisect the chord. The line is drawn through the centre of a circle to bisect a chord is perpendicular to the chord. Chapter 10 Class 9 specifies the students to learn about the number of circles that can be drawn from a single point. They have already learned the basics of this concept in the 6th class. Here a slight difference to this concept is, if the circles can be drawn from multiple points, these points are known as collinear points centre.
If we have more than two collinear points, then there is no chance to get more than a single circle. The length of the perpendicular is between the point to a line and the distance of the line.
And if the point lies on the line, the distance of the line from the point is zero. If the lengths of chords are the same, then their distance is also the same from the centre. Chords equidistant from the centre of a circle are equal in length.
These are the solved theorems for students to understand. If we draw two congruent arcs from the centre, they must be equal. The angle subtended by it at any point on the remaining part of the circle is twice of the angle subtended. In a circle, it is proved that the angles lie on a segment may not differ. The circles class 9 questions with solutions allow the students to take several benefits.
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