Class 9 | Chapter 10 | Circles | Theorem 10.12

Class 9 - Theorem 10.7
29 Aug
Class 9 - Circles, , , , , , ,

Theorem 10.12: If the sum of a pair of opposite angles of a quadrilateral is 180 degree, the quadrilateral is cyclic.

Theorem 10.11
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Prerequisite

This is relatively bit tricky theorem to prove (not difficult though) in this chapter. There are two prerequisite theorems that you must know before you solve this theorem:

Theorem 10.5 – There is (always) one and only one circle passing through three given non-collinear points.

 

Theorem 10.11 – The sum of either pair of opposite angles of a cyclic quadrilateral is 180 degrees.

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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