Class 9 | Chapter 10 | Circles | Example 6

01 Sep
Class 9 - Circles, , , , , , ,

Example 6: Prove that the quadrilateral formed (if possible) by the internal angle bisectors of any quadrilateral is cyclic.

Example 5
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Prerequisite

It is quite an interesting question to solve. The proof explained in this video tutorial used following concepts. You are recommended to understand these tutorials in case you are not aware of any of these. This question may look difficult but it us not so.

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

 

Exterior angle theorem – If a side of a triangle is produced, then the exterior angle so formed is equal to the sum of the two interior opposite angles.

 

Quadrilateral – Angle sum property – The sum of all four internal angles of a quadrilateral is always 360 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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