
01. Real Numbers
10
Lecture1.1

Lecture1.2

Lecture1.3

Lecture1.4

Lecture1.5

Lecture1.6

Lecture1.7

Lecture1.8

Lecture1.9

Lecture1.10


02. Polynomials
12
Lecture2.1

Lecture2.2

Lecture2.3

Lecture2.4

Lecture2.5

Lecture2.6

Lecture2.7

Lecture2.8

Lecture2.9

Lecture2.10

Lecture2.11

Lecture2.12


03. Linear Equation
12
Lecture3.1

Lecture3.2

Lecture3.3

Lecture3.4

Lecture3.5

Lecture3.6

Lecture3.7

Lecture3.8

Lecture3.9

Lecture3.10

Lecture3.11

Lecture3.12


04. Quadratic Equation
10
Lecture4.1

Lecture4.2

Lecture4.3

Lecture4.4

Lecture4.5

Lecture4.6

Lecture4.7

Lecture4.8

Lecture4.9

Lecture4.10


05. Arithmetic Progressions
11
Lecture5.1

Lecture5.2

Lecture5.3

Lecture5.4

Lecture5.5

Lecture5.6

Lecture5.7

Lecture5.8

Lecture5.9

Lecture5.10

Lecture5.11


06. Some Applications of Trigonometry
7
Lecture6.1

Lecture6.2

Lecture6.3

Lecture6.4

Lecture6.5

Lecture6.6

Lecture6.7


07. Coordinate Geometry
17
Lecture7.1

Lecture7.2

Lecture7.3

Lecture7.4

Lecture7.5

Lecture7.6

Lecture7.7

Lecture7.8

Lecture7.9

Lecture7.10

Lecture7.11

Lecture7.12

Lecture7.13

Lecture7.14

Lecture7.15

Lecture7.16

Lecture7.17


08. Triangles
18
Lecture8.1

Lecture8.2

Lecture8.3

Lecture8.4

Lecture8.5

Lecture8.6

Lecture8.7

Lecture8.8

Lecture8.9

Lecture8.10

Lecture8.11

Lecture8.12

Lecture8.13

Lecture8.14

Lecture8.15

Lecture8.16

Lecture8.17

Lecture8.18


09. Circles
9
Lecture9.1

Lecture9.2

Lecture9.3

Lecture9.4

Lecture9.5

Lecture9.6

Lecture9.7

Lecture9.8

Lecture9.9


10. Areas Related to Circles
12
Lecture10.1

Lecture10.2

Lecture10.3

Lecture10.4

Lecture10.5

Lecture10.6

Lecture10.7

Lecture10.8

Lecture10.9

Lecture10.10

Lecture10.11

Lecture10.12


11. Introduction to Trigonometry
9
Lecture11.1

Lecture11.2

Lecture11.3

Lecture11.4

Lecture11.5

Lecture11.6

Lecture11.7

Lecture11.8

Lecture11.9


12. Surface Areas and Volumes
9
Lecture12.1

Lecture12.2

Lecture12.3

Lecture12.4

Lecture12.5

Lecture12.6

Lecture12.7

Lecture12.8

Lecture12.9


13. Statistics
14
Lecture13.1

Lecture13.2

Lecture13.3

Lecture13.4

Lecture13.5

Lecture13.6

Lecture13.7

Lecture13.8

Lecture13.9

Lecture13.10

Lecture13.11

Lecture13.12

Lecture13.13

Lecture13.14


14. Probability
9
Lecture14.1

Lecture14.2

Lecture14.3

Lecture14.4

Lecture14.5

Lecture14.6

Lecture14.7

Lecture14.8

Lecture14.9


15. Construction
7
Lecture15.1

Lecture15.2

Lecture15.3

Lecture15.4

Lecture15.5

Lecture15.6

Lecture15.7

Chapter Notes – Construction
Some Important Points
1) To divide a line segment in a given ratio.
Construction:
Draw a line segment of length 7.6 cm and divide it in the ratio 5 : 8. Measure the two parts.Steps of Construction:
1: Draw a line segment AB = 7.6 cm
2: Draw a ray AC making any acute angle with AB, as shown in the figure.
3: On ray AC, starting from A, mark 5 + 8 = 13 equal line segments: AA1,A1A2,A2A3,A3A4,A4A5,A5A6,A6A7,A7A8,A8A9,A9A10,A10A11,A11A12,A12A13
4: Join A13B
5: From A5, draw A5P∥A13B, meeting AB at P.
6: Thus, P divides AB in the ratio 5:8.
On measuring the two parts, we find AP = 2.9 cm and PB = 4.7 cm (approx).
Justification :
In ΔABA13, PA5∥BA13
therefore, ΔABA5∼ΔABA3
⇒APPB=AA5A5A13=58
⇒APPB=58
2) To construct a triangle similar to a given triangle as per given scale factor which may be less than or may be greater than 1.
Construction:
Draw a ΔABC in which BC=6 cm, AB= 5 cm, and AC= 4 cm, Draw a triangle similar to ΔABC with its sides equal to (2/3)th of the corresponding sides of ΔABC.Steps of Construction:
1: Draw a line segment BC = 6 cm
2: With B as centre and radius equal to 5 cm, draw an arc.
3: With C as centre and radius equal to 4 cm, draw an arc intersecting the previously drawn arc at A.
4: Join AB and AC, then ΔABC is the required triangle.
5: Below BC, make an acute angle CBX.
6: Along BX, mark off three points B1,B2 and B3 BB1=B1B2=B2B3
7: Join B3C
8: From B2, Draw B2D∥B3C, meeting BC at D.
9: From D, draw ED∥AC, meeting BA at E. Then,
EBD is the required triangle whose sides are (2/3)th of the corresponding sides of ΔABC
Justification :
Since DE∥CA
therefore, ΔABC∼ΔEBD
And EBAB=BDBC=DECA=23
Hence, we get the new triangle similar to the given triangle whose sides are equal to (2/3)th of the
corresponding sides of ΔABC
3) To construct tangent at a point on a given circle.
Construction:
Draw a circle of radius 6 cm from a point 10 cm away from its centre, construct the pair of tangents to the circle and measure their length.Steps of Construction:
1: Take a point O and draw a circle of radius 6 cm.
2: Mark a point P at a distance of 10 cm from the centre O.
3: Join OP and bisect it. Let M be its mid point.
4: With M as centre and MP as radius, draw a circle to intersect the circle at Q and R.
5: Join PQ and PR. Then PQ and PR are the required tangents.
On measuring we find PQ=PR=8
Justification :
On joining OQ, We find that ∠PQO=90∘, as ∠PQO is the angle in the semicircle.
Therefore, PQ⊥OQ.
Since OQ is the radius of the given circle, so PQ has to be a tangent to the circle. Similarly, PR is also a tangent to the circle.
4) To construct the pair of tangents from an external point to a circle.
Construction:
Draw a circle of radius 3 cm. take two points P and Q on one of its extended diameter each at a distance of 7 cm from its centre. Draw tangents to the circle from these two points P and Q.Steps of Construction:
1: Take a point O, draw a circle of radius 3 cm with this point as centre.
2: Take two points P and Q on one of its extended diameter such that OP = OQ = 7 cm.
3: Bisect OP and OQ. Let their respective mid points be M1 and M2.
4: With M1 as centre and M1P as a radius, draw circle to intersect the circle at T1 and T2.
5: join PT1 and PT2. Then PT1 and PT2 are required tangents,
similarly, the tangents QT3 and QT4 can be obtained.
Justification :
On joining OT1 we find ∠PT1O=90∘ as an angle in semi circle.
Therefore, PT1⊥OT1
since OT1 is a radius of the given circle, so PT1 has to be a tangent to the circle.
similarly, PT2, QT3 and QT4 are also tangent to the circle
5 Comments
How we access live tutorial classes please tell me
For any information regarding live class please call us at 8287971571
I am not able to access any test of coordinate geometry, can you pls resolve the issue?
We have fixed the issue. Please feel free to call us at 8287971571 if you face such type of issues.
Hi!
I am a student in class 10th and ive noticed that you dont give full courses on your youtube channel. I mean, its understandable. But we request you to at least put full course of only one chapter on youtube so that we can refer to that. Only one from the book Because your videos are very good and they enrich our learning.
Please give this feedback a chance and consider our request.
Dronstudy lover,
Ananyaa