Daily Practice Problems undefined Tangents and Intersecting Chords

Question 1:

The radius of a circle is 8 cm. calculate the length of a tangent draw to this circle from a point at a distance of 10 cm from its centre. [Level: Easy]

Question 2:

Circles with centres P and Q intersect at points A and B as shown in the figure. CBD is a segment and EBM is tangent to the circle with centre Q, at point B. If the circle are congruent; show that CE = BD. [Level: Moderate]

Question 3:

Two circle of radii 5 cm and 3 cm are concentric. Calculate the length of a chord of the outer circle which touches the inner. [Level: Moderate]

Question 4:

Prove that the tangent at any point of a circle is perpendicular to the radius through the point of contact. [Level: Moderate]

Question 5:

Find the distance between two parallel tangents of a circle of radius 0.5 m. [Level: Moderate]

Question 6:

If the sides of a quadrilateral ABCD touch a circle, prove that: AB + CD = BC + AD. [Level: Easy]

Question 7:

In the figure, if AB = AC then prove that BQ = CQ. [Level: Moderate]

Question 8:

Prove that the parallelogram circumscribing a circle is a rhombus. [Level: Difficult]

Question 9:

Radii of two circles are 6. 3 cm and 3.6 cm. State the distance between their centres if:

(i) they touch each other externally

(ii) they touch each other internally [Level: Difficult]

Question 10:

Tangents AP and AQ are drawn to a circle, with centre O, from an exterior point A. Prove that: ∠PAQ = 2∠OPQ. [Level: Moderate]

Question 11:

In the given figure, AB is the diameter of the circle, with centre O, and AT is the tangent. Calculate the numerical value of x. [Level: Difficult]

Question 12:

In quadrilateral ABCD; angles D = 90°, BC = 38 cm and DC = 25 cm. A circle is inscribed in this quadrilateral which touches AB at point Q such that QB = 27 cm, Find the radius of the circle. [Level: Moderate]

Question 13:

If PQ is a tangent to the circle at R, O is the centre of the circle and ∠TRQ = 30°. Calculate ∠PRS. [Level: Moderate]

Question 14:

Tangent at P to the circumcircle of triangle PQR is drawn. If the tangent is parallel to side, QR show that ∆PQR is isosceles. [Level: Difficult]

Question 15:

Question 16:

The diameter and a chord of a circle have a common end-point. If the length of the diameter is 20 cm and the length of the chord is 12 cm, how far is the chord from the centre of the circle? [Level: Moderate]

Question 17:

In the given figure, C and D are points on the semi-circle described on AB as diameter. Given angle BAD = 70° and angle DBC = 30°. Calculate angle BDC. [Level: Easy]

Question 18:

Show that the circle drawn on any one of the equal sides of an isosceles triangle as diameter bisects the base. [Level: Moderate]

Question 19:

In the figure, AB is the chord of a circle with centre O and DOC is a line segment such that BC = DO. If ∠C = 20°, find angle AOD. [Level: Easy]

Question 20:

The given figure shows a circle with centre O and BCD is tangent to it at C. Show that: ∠ACD + ∠BAC = 90° [Level: Moderate]

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Problem-solving on ICSE 10 Maths Tangents and Intersecting Chords NCERT Chapter 18 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 Tangents and Intersecting Chords 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 Tangents and Intersecting Chords NCERT Chapter 18, 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 Tangents and Intersecting Chords 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 Tangents and Intersecting Chords 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 Tangents and Intersecting Chords. 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 Tangents and Intersecting Chords 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 Tangents and Intersecting Chords 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 Tangents and Intersecting Chords NCERT Chapter 18

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 Tangents and Intersecting Chords NCERT Chapter 18 useful.

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