Daily Practice Problems undefined Constructions (Circles)

Question 1:

Using ruler and compasses only, draw an equilateral triangle of side 4.5 cm and draw its circumscribed circle. Measure the radius of the circle. [Level: Easy]

Question 2:

Using ruler and compasses only. Construct triangle ABC, having given BC = 7cm, AB – AC = 1cm and ∠ABC = 45°. [Level: Moderate]

Question 3:

Using ruler and compasses only, draw an equilateral triangle of side 7 cm, draw its inscribed circle. Measure the radius of the circle. [Level: Moderate]

Question 4:

Draw a circle of radius 3.5 cm. mark a point P outside the circle at a distance of 6 cm from the centre. Construct two tangents from P to the given circle. Measure and write down the length of one tangent. [Level: Moderate]

Question 5:

Construct a triangle ABC in which base BC = 5.5 cm, AB = 6cm and ∠ABC = 120°.

(i) Construct a circle circumscribing the triangle ABC.

(ii) draw a cyclic quadrilateral ABCD so that D is equidistant from B and C. [Level: Moderate]

Question 6:

Construct a regular hexagon of side 4 cm. Construct a circle circumscribing the hexagon. [Level: Easy]

Question 7:

Using ruler and compasses only,

(i) Construct triangle ABC, having given BC = 7cm, AB – AC = 1cm and ∠ABC = 45°.

(ii) Inscribe a circle in the ∆ABC constructed in (i) above.

Measure its radius. [Level: Moderate]

Question 8:

Draw an inscribing circle of a regular hexagon of side 5.8 cm. [Level: Difficult]

Question 9:

Draw a circle circumscribing a regular hexagon with side 5 cm. [Level: Difficult]

Question 10:

Draw a circle of radius 4.5 cm. draw two tangents to this circle so that the angle between the tangents is 60°. [Level: Moderate]

Question 11:

Draw a circle of diameter 9 cm. mark a point at a distance of 7.5 cm from the centre of the circle. Draw tangents to the given circle from this exterior point. Measure the length of each tangent. [Level: Difficult]

Question 12:

Construct an equilateral triangle ABC with side 6 cm. Draw a circle circumscribing the triangle ABC. [Level: Moderate]

Question 13:

(i) Using ruler and compasses only, construct a triangle ABC in which AB = 8 cm, BC = 6 cm and CA = 5cm.

(ii) Find its incentre and mark it I.

(iii) With I as centre, draw a circle which will cut off 2 cm chords from each side of the triangle. What is the length of the radius of this circle. [Level: Moderate]

Question 14:

Using ruler and compasses only,

(i) Construct a triangle ABC with the following data: Base AB = 6 cm, BC = 6.2 cm and ∠CAB = 60°

(ii) In the same diagram, draw a circle which passes through the points A, B and C and mark its center O. [Level: Difficult]

Question 15:

Using ruler and compasses only, draw an equilateral triangle of side 4.5 cm and draw its circumscribed circle. Measure the radius of the circle. [Level: Easy]

Question 16:

Construct a circle, inscribing an equilateral triangle with side 5.6 cm. [Level: Moderate]

Question 17:

Using ruler and compasses only, draw an equilateral triangle of side 5 cm, draw its inscribed circle. Measure the radius of the circle. [Level: Easy]

Question 18:

Perpendicular bisectors of the sides AB and AC of a triangle ABC meet at O.

(i) What do you call the point O?

(ii) what is the relation between the distances OA, OB and OC?

(iii) Does the perpendicular bisector of BC pass through O? [Level: Moderate]

Question 19:

Using ruler and compasses only construct a triangle ABC in which BC = 4cm, ∠ACB = 45° and perpendicular from A on BC is 2.5 cm. Draw a circle circumscribing the triangle ABC and measure its radius. [Level: Easy]

Question 20:

The bisectors of angles A and B of a scalene triangle ABC meet at O.

(i) What is the point O called?

(ii) OR and OQ are drawn perpendicular to AB and CA respectively. What is the relation between OR and OQ?

(iii) What is the relation between angle ACO and angle BCO? [Level: Moderate]

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Problem-solving on ICSE 10 Maths Constructions (Circles) NCERT Chapter 19 after learning a theoretical concept is crucial for several reasons:

Application of Knowledge: Problem-solving allows you to apply the theoretical concepts of the topic ICSE 10 Maths Constructions (Circles) you have learned to real-life situations. It helps you bridge the gap between abstract knowledge and practical scenarios, making the learning more relevant and meaningful.
Understanding Deeper Concepts: When you encounter problems related to a theoretical concept that you learned in ICSE 10 Maths Constructions (Circles) NCERT Chapter 19, you are forced to delve deeper into its intricacies. This deeper understanding enhances your comprehension of the subject and strengthens your grasp of the underlying principles.
Critical Thinking: Problem-solving encourages critical thinking and analytical skills. It requires you to analyze the problem, identify relevant information, and devise a logical solution. This process sharpens your mind and improves your ability to approach complex challenges effectively.
Retention and Recall: Actively engaging in problem-solving reinforces your memory and improves long-term retention. Applying the concepts learned in Constructions (Circles) ICSE 10 Maths in practical scenarios helps you remember them better than passive reading or memorization.
Identifying Knowledge Gaps: When you attempt to solve problems, you may encounter areas where your understanding is lacking. These knowledge gaps become evident during problem-solving, and you can then focus on filling those gaps through further study and practice. You can refer Constructions (Circles) ICSE 10 Maths Notes on LearnoHub.com
Boosting Confidence: Successfully solving problems after learning a theoretical concept boosts your confidence in your abilities to handle Constructions (Circles). This confidence motivates you to tackle more challenging tasks and improves your overall performance in the subject.
Preparation for Exams and Challenges: Many exams, especially in science, mathematics, and engineering, involve problem-solving tasks. Regular practice in problem-solving prepares you to face these exams with confidence and perform well. It is also advised to take tests on Constructions (Circles) ICSE 10 Maths Online Tests at LearnoHub.com.
Enhancing Creativity: Problem-solving often requires thinking outside the box and exploring various approaches. This fosters creativity and innovation, enabling you to come up with novel solutions to different problems.
Life Skills Development: Problem-solving is a valuable life skill that extends beyond academics. It equips you with the ability to tackle various challenges you may encounter in personal and professional life.
Improving Decision Making: Problem-solving involves making decisions based on available information and logical reasoning. Practicing problem-solving enhances your decision-making skills, making you more effective in making informed choices.

In summary, problem-solving after learning a theoretical concept on CBSE Constructions (Circles) ICSE 10 Maths is an essential part of the learning process. It enhances your understanding, critical thinking abilities, and retention of knowledge. Moreover, it equips you with valuable skills that are applicable in academic, personal, and professional contexts.

You must have heard of the phrase “Practice makes a man perfect”. Well, not just a man, practice indeed enhances perfection of every individual.

Practicing questions plays a pivotal role in achieving excellence in exams. Just as the adage goes, "Practice makes perfect," dedicating time to solve a diverse range of exam-related questions yields manifold benefits. Firstly, practicing questions allows students to familiarize themselves with the exam format and types of problems they might encounter. This familiarity instills confidence, reducing anxiety and improving performance on the actual exam day. Secondly, continuous practice sharpens problem-solving skills and enhances critical thinking, enabling students to approach complex problems with clarity and efficiency. Thirdly, it aids in identifying weak areas, allowing students to focus their efforts on improving specific topics. Moreover, practice aids in memory retention, as active engagement with the material reinforces learning. Regular practice also hones time management skills, ensuring that students can allocate appropriate time to each question during the exam. Overall, practicing questions not only boosts exam performance but also instills a deeper understanding of the subject matter, fostering a holistic and effective learning experience.

All About Daily Practice Problems on ICSE 10 Maths Constructions (Circles) NCERT Chapter 19

Our Daily Practice Problems (DPPs) offer a diverse range of question types, including Multiple Choice Questions (MCQs) as well as short and long answer types. These questions are categorized into Easy, Moderate, and Difficult levels, allowing students to gradually progress and challenge themselves accordingly. Additionally, comprehensive solutions are provided for each question, available for download in PDF format - Download pdf solutions as well as Download pdf Questions. This approach fosters a holistic learning experience, catering to different learning styles, promoting self-assessment, and improving problem-solving skills. With our well-structured DPPs, students can excel in exams while gaining a deeper understanding of the subject matter. Hope you found the content on ICSE 10 Maths Constructions (Circles) NCERT Chapter 19 useful.

Last but not least, to get the best hold on ICSE 10 Maths Constructions (Circles) NCERT Chapter 19, do not forget to check out:

Constructions (Circles) ICSE 10 Maths Best videos
Constructions (Circles) ICSE 10 Maths NCERT Solutions
ICSE 10 Maths Constructions (Circles) Revision notes
Constructions (Circles) ICSE 10 Maths DPPs, Download PDF of solutions
ICSE 10 Maths Constructions (Circles) Online Tests
ICSE 10 Maths Sample papers