NCERT solution Class 10 circles

NCERT Solutions

Class 10 Maths

Circles

NCERT Questions

Ex.10.1 Q.1
Ex.10.1 Q.2
Ex.10.1 Q.3
Ex.10.1 Q.4
Ex.10.2 Q.1
Ex.10.2 Q.2
Ex.10.2 Q.3
Ex.10.2 Q.4
Ex.10.2 Q.5
Ex.10.2 Q.6
Ex.10.2 Q.7
Ex.10.2 Q.8
Ex.10.2 Q.9
Ex.10.2 Q.10
Ex.10.2 Q.11
Ex.10.2 Q.12
Ex.10.2 Q.13

Ex.10.2 Q.12

A triangle ABC is drawn to circumscribe a circle of radius 4 cm such that the segments BD and DC into

which BC is divided by the point of contact D are of lengths 8 cm and 6 cm respectively (see Fig. 10.14).

Find the sides AB and AC.

Let the given circle touch the sides AB and AC of the triangle at point E and F respectively

and the length of the line segment AF be x.

In ΔABC,

CF = CD = 6cm

(Tangents on the circle from point C)

BE = BD = 8cm

(Tangents on the circle from point B)

AE = AF = x

(Tangents on the circle from point A)

AB = AE + EB = x + 8

BC = BD + DC = 8 + 6 = 14

CA = CF + FA = 6 + x

Now, 2s = AB + BC + CA

= x + 8 + 14 + 6 + x

= 28 + 2x

=> s = 14 + x

Area of ΔABC = √ {s (s - a) (s - b) (s - c)}

= √ [(14 + x) {14 + x - 14} {(14 + x) – (6 + x)} {(14 + x) – (8 + x)}]

= √ [(14 + x) × x × 8 × 6]

= 4√ [3(14x + x²)]

Area of ΔOBC = × OD × BC

= × 4 × 14

= 28

Area of ΔOCA = × OF × AC

= × 4 × (6 + x)

= 2 × (6 + x)

= 12 + 2x

Area of ΔOAB = × OE × AB

= × 4 × (8 + x)

= 2 × (8 + x)

= 16 + 2x

Now, Area of ∆ABC = Area of ∆OBC + Area of ∆OCA + Area of ∆OAB

=> 4√ [3(14x + x²)] = 28 + 12 + 2x + 16 + 2x

=> 4√ [3(14x + x²)] = 56 + 4x

=> 4√ [3(14x + x²)] = 4(14 + x)

=> √ [3(14x + x²)] = 14 + x

Squaring on both sides, we get

=> 3(14x + x²) = (14 + x)²

=> 42x + 3x² = 196 + x² + 28x

=> 42x + 3x² - 196 - x² - 28x = 0

=> 2x² + 14x – 196 = 0

=> x² + 7x – 98 = 0

=> x² + 14x - 7x - 98 = 0

=> x (x + 14) – 7(x + 14) = 0

=> (x - 7) (x + 14) = 0

=> x = 7, -14

Here, x = -14 is not possible as the length of the sides will be negative.

So, x = 7

Hence, AB = x + 8 = 7 + 8 = 15 cm

CA = 6 + x = 6 + 7 = 13 cm

Video solution:

Circles Class 10 Maths NCERT Chapter 10 NCERT Solutions

Solving NCERT textbook questions of Circles Class 10 Maths NCERT Chapter 10 is a crucial step to gauge your understanding of the concepts. It provides you with an opportunity to assess your grasp of the material after learning each chapter. We have already provided solutions to all the exercises in the NCERT textbook of Class 10 Maths Circles, available in various formats such as video, text, and downloadable PDFs. If you need assistance with any of the NCERT questions or any other academic topics, feel free to ask in the “Ask Questions” section of LearnoHub.com.

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Attempt to Solve Yourself: Before looking at the solution, try to solve or answer the question independently. This practice will help you test your knowledge and problem-solving skills.
Match with Our Solution: After attempting the question, compare your result and approach with the provided NCERT solution. This step allows you to identify any mistakes or gaps in your understanding.
Refer to Solution Video (if needed): If you encounter difficulty or are unable to solve a question, you can refer to the NCERT solution video on Circles Class 10 Maths NCERT Chapter 10 to get a step-by-step explanation of the correct approach. Pay attention to the reasoning and methodology used in the video.
Solve Again Yourself: Once you've understood the solution, attempt to solve the question again by yourself. Repetition and practice solidify your understanding of the concepts and improve retention.
Avoid Memorization: Focus on understanding the underlying principles and concepts behind each solution. Avoid simply memorizing the solutions, as this may hinder your ability to apply the knowledge in different contexts.
Attempt All Questions: Make an effort to attempt all the questions provided in the NCERT textbook. This comprehensive practice will help you cover the entire syllabus and reinforce your understanding across various topics. You may refer Class 10 Maths Circles Online Test on LearnoHub.com.
Review and Revise: Regularly review the concepts and solutions you've learned. Revise your notes and practice regularly to retain the knowledge effectively. You may refer Circles Class 10 Maths Notes.
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NCERT solutions of Circles Class 10 Maths - all questions of all exercises are solved. Q. No. 1, 2, 3, and so on. Complete explanation and detailed solution makes them the best videos for Class 10 Maths Circles NCERT solutions.