Circles Theorems and Defination | Chord and chords of a Circle Properties | CBSE Class 9

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00:02 CBSE solutions for class 9 maths circles Q1. Fill in the blanks:

(i) The centre of a circle lies in of the circle. (exterior/ interior)

00:29 Regions of Circle.(Exterior region and Interior region).

00:50 (ii) A point, whose distance from the centre of a circle is greater than its radius lies in of the circle. (exterior/ interior)

01:50 (iii) The longest chord of a circle is a of the circle.

01:59 Defination Diameter of a circle.

02:40 (iv) An arc is a when its ends are the ends of a diameter.

03:00 Defination of Semi-circle.

03:16 (v) Segment of a circle is the region between an arc and of the circle.

03:30 (vi) A circle divides the plane, on which it lies, in parts.

03:59 Q2. Write True or False: Give reasons for your answers.

(i) Line segment joining the centre to any point on the circle is a radius of the circle.

04:30 (ii) A circle has only finite number of equal chords.

05:05 (iii) If a circle is divided into three equal arcs, each is a major arc.

05:10 Major Arc & Minor Arc

05:48 (iv) A chord of a circle, which is twice as long as its radius, is a diameter of the circle.

05:59 Defination of Chord , Diameter .

06:10 (v) Sector is the region between the chord and its corresponding arc.

06:18 Defination of Sector , Segment.

06:55 (vi) A circle is a plane figure.

Angle Subtended by a Chord at a Point

07: 13 Q1. Recall that two circles are congruent if they have the same radii. Prove that equal

chords of congruent circles subtend equal angles at their centres.

09:04 By using S.S.S rule of Congruency

09:09 Apply CPCT (Corresponding Parts of Congruent Triangles)

09:34 CBSE class 10 maths chapter 10 Circles Q2. Prove that if chords of congruent circles subtend equal angles at their centres, then

the chords are equal.

11:11 Apply S.S.S rule of Congruency

There is one and only one circle passing through three given non-collinear points.

11:41 CBSE Class 9 maths solutions Circles Q1. Draw different pairs of circles. How many points does each pair have in common?

What is the maximum number of common points

12:09 Pair of Circles with no point of intersection in common.

12:25 Pair of Circles with one point of intersection in common.

12:45 Pair of Circles with two points of intersection in common.

13:15 Conclusion

13:30 CBSE class 10 maths chapter 10 Circles Q3. If two circles intersect at two points, prove that their centres lie on the perpendicular bisector of the common chord.

15:30 Apply S.S.S rule of Congruency

15:50 Apply CPCT (Corresponding Parts of Congruent Triangles)

16:53 Apply S.A.S rule of Congruency

17:06 Apply CPCT

17:30 Using Linear Pair

Equal Chords and Their Distances from the Centre

The length of the perpendicular from a point to a line is the distance of the line from the point .

Equal chords of a circle ( or of congruent circles) are equidistant from the centre(or centres).

Chords equidistant from the centre of a circle are equal in length.

18:40 CBSE class 10 maths chapter 10 Circles Q1. Two circles of radii 5 cm and 3 cm intersect at two points and the distance between their centres is 4 cm. Find the length of the common chord.

20:33 Using Theorem:If two circles intersect at two points, prove that their centres lie on the perpendicular bisector of the common chord.

21:13 CBSE class 10 maths chapter 10 Circles Q2. If two equal chords of a circle intersect within the circle, prove that the segments of one chord are equal to corresponding segments of the other chord.

22:00 Construction to solve the theorem.

23:13 Apply R.H.S rule of Congruency

26:39 CBSE class 10 maths chapter 10 Circles Q3. If two equal chords of a circle intersect within the circle, prove that the line joining the point of intersection to the centre makes equal angles with the chords.

28:52 Equal chords of a circle ( or of congruent circles) are equidistant from the centre(or centres)

Q4 If a line intersects two concentric circles (circles with the same centre) with centre O at A, B, C and D, prove that AB = CD (see Fig. 10.25).

31:15 The line drawn through the centre of a circle to bisect a chord is perpendicular to the chord.

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