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Theorem 10.8: The angle subtended by an arc at the centre is double the angle subtended by it at any point on the remaining part of the circle.

Theorem 10.7
Theorem 10.9

This is a very important theorem on circles in geometry. It is used quite a lot to prove many more theorems on circles. In this tutorial, this theorem has been explained using two approaches:

  1. Angle sum property of triangle
  2. Exterior angle theorem 

Chapter 10 – Circles

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Theorems

Theorem 10.1

Theorem 10.2

Theorem 10.3

Theorem 10.4

Theorem 10.5

Theorem 10.6

Theorem 10.7

Theorem 10.8

Theorem 10.9

Theorem 10.10

Theorem 10.11

Theorem 10.12

Exercise 10.1

Question 1 & 2

Exercise 10.2

Question 1

Question 2

Exercise 10.3

Question 1

Question 2

Question 3

Exercise 10.4

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Exercise 10.5

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Question 7

Question 8

Question 9

Question 10

Question 11

Question 12

Examples

Example 1

Example 2

Example 3

Example 4

Example 5

Example 6

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