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### Theory

 1 Introduction 2 Tangent to a circle 3 Results 1 and 2 on circles and tangents 4 Result 3 on circles and tangents 5 Result 4 on circles and tangents 6 Result 5 on circles and tangents 7 Result 6 on circles and tangents 8 Alternate Segment Theorem 9 Construction of a tangent to a circle using its centre 10 Construction of a tangent to a circle using alternate segment theorem 11 Construction of a pair of tangents to a circle from an external point 12 Congruency theorems

### Exercises

 1 Find the radius of the circle Difficulty: easy 2 2 Find the value of 'x' Difficulty: easy 1 3 Find the length as directed Difficulty: easy 2 4 Find the sides of an equilateral triangle Difficulty: easy 2 5 Find the length Difficulty: easy 1 6 Find the length of the tangent Difficulty: medium 3 7 Find the value of 'y' Difficulty: medium 3 8 Find the unknown angle Difficulty: medium 3 9 Find the length of the chord Difficulty: medium 3 10 Find the radius of the larger circle Difficulty: medium 3 11 Find the angle Difficulty: medium 3 12 Find the length of the left out portion Difficulty: medium 3 13 Find the value of 'x', 'y' and 'z' Difficulty: hard 6 14 Find the length of the required tangent Difficulty: hard 4 15 Find the length of the required segment Difficulty: hard 4 16 Find the value of 'x' and 'y' Difficulty: hard 4

### Tests

 1 Training test I Difficulty: medium 7 2 Training test II Difficulty: medium 7

### Teacher manual

 1 Methodical recommendation