Chords Archives – Mathemafia http://sh016.global.temp.domains/~mathemaf/tag/chords/ Mathematics is like music - Enjoy it!!! Thu, 03 Sep 2020 12:50:22 +0000 en-US hourly 1 https://wordpress.org/?v=7.1 https://mathemafia.com/wp-content/uploads/2020/08/cropped-M__Logo__SM-1-32x32.png Chords Archives – Mathemafia http://sh016.global.temp.domains/~mathemaf/tag/chords/ 32 32 Class 9 | Chapter 10 | Circles | Exercise 10.5 | Question 6 https://mathemafia.com/class-9-chapter-10-circles-exercise-10-5-question-6/ Wed, 02 Sep 2020 05:31:16 +0000 http://sh016.global.temp.domains/~mathemaf/?p=1576 Question 6: ABCD is a cyclic quadrilateral whose diagonals intersect at a point E. If ∠ DBC = 70°, ∠ BAC is 30°, find ∠ BCD. Further, if AB = BC, find ∠ ECD. Question 5 Question 7 Prerequisite Most…

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Question 6: ABCD is a cyclic quadrilateral whose diagonals intersect at a point E. If ∠ DBC = 70°, ∠ BAC is 30°, find ∠ BCD. Further, if AB = BC, find ∠ ECD.

Question 5
Question 7

Prerequisite

Most of the questions in this exercise are based on the theorem – same segment angles are equal. We have also used the Isosceles triangle theorem in to solve this question along with the angle sum property of a triangle.

Theorem 10.9: Angles in the same segment of a circle are equal

 

Theorem 7.2: Angles opposite to equal sides of an isosceles triangle are equal.

 

Theorem 6.7: The sum of the angles of a triangle is 180º.

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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]]> Class 9 | Chapter 10 | Circles | Exercise 10.5 | Question 5 https://mathemafia.com/class-9-chapter-10-circles-exercise-10-5-question-5/ Wed, 02 Sep 2020 05:31:13 +0000 http://sh016.global.temp.domains/~mathemaf/?p=1575 Question 5: In Fig. 10.39, A, B, C and D are four points on a circle. AC and BD intersect at a point E such that ∠ BEC = 130°and ∠ ECD = 20°. Find ∠ BAC. Question 4 Question…

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Question 5: In Fig. 10.39, A, B, C and D are four points on a circle. AC and BD intersect at a point E such that ∠ BEC = 130°and ∠ ECD = 20°. Find ∠ BAC.

Question 4
Question 6

Prerequisite

Again, same concept – Angles in same segment are equal. Also used is the exterior angle theorem to solve this easy question. Below are the video tutorials that you may watch just in case you need to revise these concepts.

Theorem 10.9: Angles in the same segment of a circle are equal

 

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.

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

The post Class 9 | Chapter 10 | Circles | Exercise 10.5 | Question 5 appeared first on Mathemafia.

]]> Class 9 | Chapter 10 | Circles | Exercise 10.5 | Question 4 https://mathemafia.com/class-9-chapter-10-circles-exercise-10-5-question-4/ Tue, 01 Sep 2020 08:11:37 +0000 http://sh016.global.temp.domains/~mathemaf/?p=1555 Question 4: In Fig. 10.38, ∠ ABC = 69°, ∠ ACB = 31°, find ∠ BDC. Question 3 Question 5 Prerequisite Simple! Concepts used: Angle sum property of triangle Angles in the same segment of a circle are equal Theorem…

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Question 4: In Fig. 10.38, ∠ ABC = 69°, ∠ ACB = 31°, find ∠ BDC.

Question 3
Question 5

Prerequisite

Simple!

Concepts used:

  • Angle sum property of triangle
  • Angles in the same segment of a circle are equal

Theorem 10.9: Angles in the same segment of a circle are equal

 

Theorem 6.7: The sum of the angles of a triangle is 180º.

Chapter 10 – Circles

​

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

The post Class 9 | Chapter 10 | Circles | Exercise 10.5 | Question 4 appeared first on Mathemafia.

]]> Class 9 | Chapter 10 | Circles | Exercise 10.5 | Question 3 https://mathemafia.com/class-9-chapter-10-circles-exercise-10-5-question-3/ Tue, 01 Sep 2020 08:11:32 +0000 http://sh016.global.temp.domains/~mathemaf/?p=1554 Question 3: In Fig. 10.37, ∠ PQR = 100°, where P, Q and R are points on a circle with centre O. Find ∠ OPR. Question 2 Question 4 Prerequisite Questions are always easy to solve. All you need to…

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Question 3: In Fig. 10.37, ∠ PQR = 100°, where P, Q and R are points on a circle with centre O. Find ∠ OPR.

Question 2
Question 4

Prerequisite

Questions are always easy to solve. All you need to do is visualise the different possibilities and move ahead. Just like, previous questions, we will apply the following theorem in this question.

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.

 
The other very easy concept that has been used to solve this question is Isosceles Triangle Theorem.
 

Chapter 10 – Circles

​

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

The post Class 9 | Chapter 10 | Circles | Exercise 10.5 | Question 3 appeared first on Mathemafia.

]]> Class 9 | Chapter 10 | Circles | Exercise 10.5 | Question 2 https://mathemafia.com/class-9-chapter-10-circles-exercise-10-5-question-2/ Tue, 01 Sep 2020 08:11:27 +0000 http://sh016.global.temp.domains/~mathemaf/?p=1553 Question 2: A chord of a circle is equal to the radius of the circle. Find the angle subtended by the chord at a point on the minor arc and also at a point on the major arc. Question 1…

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Question 2: A chord of a circle is equal to the radius of the circle. Find the angle subtended by the chord at a point on the minor arc and also at a point on the major arc.

Question 1
Question 3

Prerequisite

The chord of the size of radius makes an equilateral triangle. That gives us the angle subtended for the corresponding chord at the centre. Rest is applying the following theorem to solve this question.

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.

 

Different types of angles: In case you have any doubts about the different types of angles (like reflex angle, used in this question), you are recommended to watch the following video tutorial.

Chapter 10 – Circles

​

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

The post Class 9 | Chapter 10 | Circles | Exercise 10.5 | Question 2 appeared first on Mathemafia.

]]> Class 9 | Chapter 10 | Circles | Exercise 10.5 | Question 1 https://mathemafia.com/class-9-chapter-10-circles-exercise-10-5-question-1/ Tue, 01 Sep 2020 08:08:28 +0000 http://sh016.global.temp.domains/~mathemaf/?p=1550 Question 1: In Fig. 10.36, A,B and C are three points on a circle with centre O such that ∠ BOC = 30° and ∠ AOB = 60°. If D is a point on the circle other than the arc…

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Question 1: In Fig. 10.36, A,B and C are three points on a circle with centre O such that ∠ BOC = 30° and ∠ AOB = 60°. If D is a point on the circle other than the arc ABC, find ∠ADC.

Ex: 10.4 | Question 6
Question 2

Prerequisite

This is the simplest question of this exercise. Below is the link of the page and video tutorial of the theorem that we used to solve this question.

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.

 

Chapter 10 – Circles

​

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

The post Class 9 | Chapter 10 | Circles | Exercise 10.5 | Question 1 appeared first on Mathemafia.

]]> Class 9 | Chapter 10 | Circles | Exercise 10.4 | Question 6 https://mathemafia.com/class-9-chapter-10-circles-exercise-10-4-question-6/ Tue, 18 Aug 2020 06:09:52 +0000 http://sh016.global.temp.domains/~mathemaf/?p=1428 Question 6: A circular park of radius 20m is situated in a colony. Three boys Ankur, Syed and David are sitting at equal distance on its boundary each having a toy telephone in his hands to talk each other. Find…

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Question 6: A circular park of radius 20m is situated in a colony. Three boys Ankur, Syed and David are sitting at equal distance on its boundary each having a toy telephone in his hands to talk each other. Find the length of the string of each phone.

Question 5
Ex: 10.5 | Question 1

Chapter 10 – Circles

​

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

The post Class 9 | Chapter 10 | Circles | Exercise 10.4 | Question 6 appeared first on Mathemafia.

]]> Class 9 | Chapter 10 | Circles | Exercise 10.4 | Question 5 https://mathemafia.com/class-9-chapter-10-circles-exercise-10-4-question-5/ Tue, 18 Aug 2020 06:09:47 +0000 http://sh016.global.temp.domains/~mathemaf/?p=1427 Question 5: Three girls Reshma, Salma and Mandip are playing a game by standing on a circle of radius 5m drawn in a park. Reshma throws a ball to Salma, Salma to Mandip, Mandip to Reshma. If the distance between…

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Question 5: Three girls Reshma, Salma and Mandip are playing a game by standing on a circle of radius 5m drawn in a park. Reshma throws a ball to Salma, Salma to Mandip, Mandip to Reshma. If the distance between Reshma and Salma and between Salma and Mandip is 6m each, what is the distance between Reshma and Mandip?

Question 4
Question 6

Chapter 10 – Circles

​

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

The post Class 9 | Chapter 10 | Circles | Exercise 10.4 | Question 5 appeared first on Mathemafia.

]]> Class 9 | Chapter 10 | Circles | Exercise 10.4 | Question 4 https://mathemafia.com/class-9-chapter-10-circles-exercise-10-4-question-4/ Tue, 18 Aug 2020 06:09:43 +0000 http://sh016.global.temp.domains/~mathemaf/?p=1426 Question 4: If a line intersects two concentric circles (circles with the same centre) with centre O at A, B, C and D, prove that AB = CD (see Fig. 10.25). Question 3 Question 5

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Question 4: If a line intersects two concentric circles (circles with the same centre) with centre O at A, B, C and D, prove that AB = CD (see Fig. 10.25).

Question 3
Question 5

Chapter 10 – Circles

​

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

The post Class 9 | Chapter 10 | Circles | Exercise 10.4 | Question 4 appeared first on Mathemafia.

]]> Class 9 | Chapter 10 | Circles | Exercise 10.4 | Question 3 https://mathemafia.com/class-9-chapter-10-circles-exercise-10-4-question-3/ Tue, 18 Aug 2020 06:09:38 +0000 http://sh016.global.temp.domains/~mathemaf/?p=1425 Question 3: If two equal chords of a circle intersect within the circle, prove that the line joining the point of intersection to the centre makes equal angles with the chords. Question 2 Question 4

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Question 3: If two equal chords of a circle intersect within the circle, prove that the line joining the point of intersection to the centre makes equal angles with the chords.

Question 2
Question 4

Chapter 10 – Circles

​

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

The post Class 9 | Chapter 10 | Circles | Exercise 10.4 | Question 3 appeared first on Mathemafia.

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