Circles Theorems and Defination | Chord and chords of a Circle Properties | CBSE Class 9
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.
13:30 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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