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Methodical recommendation:
Theory
| Number | Name | Description |
|---|---|---|
| 1. | Introduction | To recall the concept of circles and tangents. |
| 2. | Tangent to a circle | To learn what is a tangent and its real life examples. |
| 3. | Results 1 and 2 on circles and tangents | To learn and understand the results on circles and tangents. |
| 4. | Result 3 on circles and tangents | To learn and understand the results on circles and tangents. |
| 5. | Result 4 on circles and tangents | To learn and understand the results on circles and tangents. |
| 6. | Result 5 on circles and tangents | To learn and understand the results on circles and tangents. |
| 7. | Result 6 on circles and tangents | To learn and understand the results on circles and tangents. |
| 8. | Alternate Segment Theorem | To learn and understand the Alternate Segment Theorem. |
| 9. | Construction of a tangent to a circle using its centre | To learn how to construct a tangent to a circle using its centre. |
| 10. | Construction of a tangent to a circle using alternate segment theorem | To learn how to construct a tangent to a circle using alternate segment theorem. |
| 11. | Construction of a pair of tangents to a circle from an external point | To learn how to construct a pair of tangents to a circle from an external point of the circle. |
| 12. | Congruency theorems | To learn the congruency theorems based on a triangle. |
Textbook Questions
| Number | Name | Type | Difficulty | Marks | Description |
|---|---|---|---|---|---|
| 1. | Multiple choice question I | Other | easy | 1 m. | In this exercise, choose the correct answer based on the properties of circle and tangents. |
| 2. | Multiple choice question II | Other | easy | 1 m. | In this exercise, choose the correct answer based on the properties of circle and tangents. |
| 3. | Multiple choice question III | Other | easy | 1 m. | In this exercise, choose the correct answer based on the properties of circle and tangents. |
| 4. | Multiple choice question IV | Other | easy | 1 m. | In this exercise, choose the correct answer based on the properties of circle and tangents. |
| 5. | Multiple choice question V | Other | easy | 1 m. | In this exercise, choose the correct answer based on the properties of circle and tangents. |
| 6. | Two marks example problem I | Other | medium | 2 m. | Work on the problem to find the answers using the properties of circles and tangents. |
| 7. | Two marks example problem II | Other | medium | 2 m. | Work on the problem to find the answers using the properties of circles and tangents. |
| 8. | Two marks example problem III | Other | medium | 2 m. | Work on the problem to find the answers using the properties of circles and tangents. |
| 9. | Two marks example problem IV | Other | medium | 2 m. | Work on the problem to find the answers using the properties of circles and tangents. |
| 10. | Two marks exercise problem I | Other | medium | 2 m. | Work on the problem to find the answers using the properties of circle and tangents. |
| 11. | Two marks exercise problem II | Other | medium | 2 m. | Work on the problem to find the answers using the properties of circle and tangents. |
| 12. | Two marks exercise problem III | Other | medium | 2 m. | Work on the problem to find the answers using the properties of circle and tangents. |
| 13. | Two marks exercise problem IV | Other | medium | 2 m. | Work on the problem to find the answers using the properties of circle and tangents. |
| 14. | Five marks example problem I | Other | medium | 5 m. | Work on the problems to find the answer using the properties of circle and tangents. |
| 15. | Five marks example problem II | Other | medium | 10 m. | Work on the problems to find the answer using the properties of circle and tangents. |
| 16. | Five marks exercise problem III | Other | hard | 5 m. | Try to answer the questions using the properties of circles and tangents. |
| 17. | Five marks exercise problem IV | Other | hard | 5 m. | Try to answer the questions using the properties of circles and tangents. |
| 18. | Five marks exercise problem V | Other | hard | 5 m. | Try to answer the questions using the properties of circles and tangents. |
| 19. | Five marks exercise problem VI | Other | hard | 5 m. | Try to answer the questions using the properties of circle and tangents. |
| 20. | Five marks exercise problem VII | Other | hard | 5 m. | Try to answer the questions using the properties of circle and tangents. |
| 21. | Five marks exercise problem VIII | Other | hard | 5 m. | Try to answer the questions using the properties of circle and tangents. |
| 22. | Five marks exercise problem IX | Other | hard | 5 m. | To prove the given statement using Ceva's theorem. |
| 23. | Five marks exercise problem X | Other | hard | 5 m. | To prove the given statement using Ceva's theorem. |
| 24. | Five marks exercise problem XI | Other | hard | 5 m. | To prove the given statement using Ceva's theorem. |
| 25. | Eight mark example problem I | Other | hard | 8 m. | Try to construct a tangent to a circle using the centre. |
| 26. | Eight mark example problem II | Other | hard | 8 m. | Try to construct a tangent to a circle using the alternate segment theorem. |
| 27. | Eight mark example problem III | Other | hard | 8 m. | Try to construct a pair of tangents to a circle from an external point P. |
| 28. | Eight mark exercise problem I | Other | hard | 8 m. | Try to construct a tangent to a circle using the centre. |
| 29. | Eight mark exercise problem II | Other | hard | 8 m. | Try to construct a tangent to a circle using the alternate segment theorem. |
| 30. | Eight mark exercise problem III | Other | hard | 8 m. | Try to construct a pair of tangents to a circle from an external point P. |
| 31. | Eight mark exercise problem IV | Other | hard | 4 m. | Try to construct a pair of tangents to a circle from an external point P. |
| 32. | Eight mark exercise problem V | Other | hard | 8 m. | Try to construct a pair of tangents to a circle from an external point P. |
| 33. | Eight mark exercise problem VI | Other | hard | 8 m. | Try to construct a pair of tangents to a circle from an external point P. |
Practice Questions
| Number | Name | Type | Difficulty | Marks | Description |
|---|---|---|---|---|---|
| 1. | Find the value of 'x' | Other | easy | 1 m. | To find the value of 'x' from the given figure. |
| 2. | Find the length as directed | Other | easy | 2 m. | To find the length of the tangent from the measurements provided. |
| 3. | Find the sides of an equilateral triangle | Other | easy | 2 m. | To find the measure of the side of an equilateral triangle using the property of circles and tangents. |
| 4. | Find the length | Other | easy | 2 m. | To find the given length using the property of the tangent to the circle. |
| 5. | Find the length of the tangent | Other | medium | 3 m. | To find the length of the tangent using the using result of the tangent on a circle. |
| 6. | Find the unknown angle | Other | medium | 3 m. | To find the unknown angle using the given information. |
| 7. | Find the radius of the larger circle | Other | medium | 3 m. | To find the radius of the larger circle using the result of the tangent on a circle. |
| 8. | Find the angle | Other | medium | 3 m. | To find the unknown angle from the data provided. |
| 9. | Find the length of the left out portion | Other | medium | 3 m. | To find the length of the left out portion using the congruency theorem based on a triangle. |
| 10. | Find the value of 'x', 'y' and 'z' | Other | hard | 6 m. | To find the value of 'x', 'y' and 'z' from the measurements provided. |
| 11. | Find the length of the required tangent | Other | hard | 4 m. | To find the length of the tangent using the using result of the tangent on a circle. |
| 12. | Find the value of 'x' and 'y' | Other | hard | 4 m. | To find the length of the left out portion using the congruency theorem based on a triangle. |
Key Questions for School Exam Preparation
| Number | Name | Type | Difficulty | Marks | Description |
|---|---|---|---|---|---|
| 1. | Find the length of BC | Other | medium | 2 m. | Work on the problem to find the answer using the properties of circles and tangents. |
| 2. | Find AD, BE and CF | Other | hard | 5 m. | Try to answer the questions using the properties of circles and tangents. |
| 3. | Determine the radius of the circle | Other | hard | 5 m. | Try to answer the questions using the properties of circles and tangents. |
Questions for Teacher Use
| Number | Name | Type | Difficulty | Marks | Description |
|---|---|---|---|---|---|
| 1. | Tangent of a circle | Other | medium | 1 m. | Work on the problem to find the answers using the properties of circles and tangents. |
| 2. | Radius of the circle | Other | medium | 1 m. | Work on the problem to find the answers using the properties of circle and tangents. |
| 3. | Find the length of the tangent | Other | medium | 1 m. | To find the length of the tangent using the using result of the tangent on a circle. |
| 4. | Find the radius of the circle | Other | easy | 2 m. | To find the radius of the circle using the results on tangent to the circle. |
| 5. | Find the value of 'y' | Other | medium | 3 m. | To find the value of 'y' from the given figure. |
| 6. | Find the length of the chord | Other | medium | 3 m. | To find the length of the chord using the using result of the tangent on a circle. |
| 7. | Construct a tangent to a circle using its centre | Other | medium | 5 m. | To construct a tangent to a circle using its centre. |
| 8. | Find the length of the required segment | Other | hard | 4 m. | To find the length of required segment using the using Menelaus theorem. |
| 9. | Construct a tangent to a circle using alternate segment theorem | Other | hard | 6 m. | To construct a tangent to a circle using alternate segment theorem. |
| 10. | Construct of a pair of tangents to a circle from an external point | Other | hard | 6 m. | To construct a pair of tangents to a circle from an external point of the circle. |
| 11. | Determine the tangent length | Other | medium | 1 m. | Work on the problem to find the answers using the properties of circles and tangents. |
| 12. | Length of the chord | Other | medium | 1 m. | Work on the problem to find the answers using the properties of circles and tangents. |
| 13. | Calculate the angle | Other | medium | 1 m. | Work on the problem to find the answers using the properties of circle and tangents. |
| 14. | Find the sides of an equilateral triangle | Other | easy | 1 m. | To find the measure of the side of an equilateral triangle using the property of circles and tangents. |
| 15. | Circles and tangents | Other | easy | 1 m. | In this exercise, choose the correct answer based on the properties of circle and tangents. |
Periodic assessments
| Number | Name | Recomended time: | Difficulty | Marks | Description |
|---|---|---|---|---|---|
| 1. | Homework I | 00:20:00 | easy | 9 m. | |
| 2. | Homework II | 00:20:00 | easy | 12 m. | |
| 3. | Homework III | 00:20:00 | medium | 12 m. | |
| 4. | Homework IV | 00:25:00 | medium | 13 m. | |
| 5. | Revision test I | 00:25:00 | medium | 14 m. | |
| 6. | Revision test II | 00:25:00 | medium | 15 m. | |
| 7. | Revision test III | 00:25:00 | hard | 15 m. | |
| 8. | Revision test IV | 00:35:00 | hard | 23 m. | |
| 9. | Revision test V | 00:40:00 | hard | 30 m. | |
| 10. | Periodic Assessment | 00:10:00 | medium | 6 m. | PA 2 |
| 11. | Periodic Assessment - Extended version | 00:10:00 | medium | 8 m. | PA 2 |
| 12. | Periodic Assessment - 3 | 00:10:00 | medium | 2 m. | PA3 |
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