Class 9 Maths
Circles
Question 1:
A _____ is the longest chord and all _____ have the same length, which is equal to two times the radius.
Question 2:
Prove that equal chords of a circle subtend equal angles at the centre.
Question 3:
The line drawn through the centre of a circle to bisect a chord is perpendicular to the chord.
Question 4:
The sum of either pair of opposite angles of a cyclic quadrilateral is 180°.
Question 5:
In the figure, O is the centre of a circle passing through points A, B, C and D and ∠ADC = 120°. Find the value of x.
Question 6:
In the figure, ABCD is a cyclic quadrilateral in which AC and BD are its diagonals. If ∠DBC = 55° and ∠BAC = 45°, find ∠BCD.
Question 7:
Two circles intersect at two points A and B. AD and AC are diameters to the two circles as shown in the figure. Prove that B lies on the line segment DC.
Question 8:
In the given figure, O is the centre of the circle, ∠AOB = 60° and CDB = 90°. Find ∠OBC.
Question 9:
In the given figure, O is the centre of the circle with chords AP and BP being produced to R and Q respectively. If ∠QPR = 35°, find the measure of ∠AOB.
Question 10:
Two circles of radii 5 cm and 3 cm intersect at two points and the distance between their centres is 4 cm. Find the length of the common chord.
Question 11:
In the given figure, ∠ACP = 40° and BPD = 120°, then find ∠CBD.
Question 12:
If the diagonals of a cyclic quadrilateral are diameters of the circle through the opposite vertices of the quadrilateral. Prove that the quadrilateral is a rectangle.
Question 13:
The angle subtended by the diameter of a semi-circle is _____.
Question 14:
The length of the complete circle is called ____.
Question 15:
Which of the following is correct statement?
(i) The centre of the circle lies outside of the circle.
(ii) The longest chord of the circle is any chord of the circle.
(iii) A circle has only finite number of chords.
(iv) From a point on the circle, only one tangent has been drawn.
Question 16:
Number of circles that can be drawn through three non-collinear points is
Question 17:
In the figure, dotted region AOB is called ______.
Question 18:
If AB = 12 cm, BC = 16 cm and AB is perpendicular to BC then radius of the circle is _____.
Question 19:
In the given figure, BC is the diameter of the circle and ∠BAO = 60°. Then ∠ADC is equal to
Question 20:
In the figure, ∠PQR = 1000, where P, Q and R are points on a circle with centre O. Find ∠OPR.
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In summary, problem-solving after learning a theoretical concept on CBSE Circles Class 9 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.
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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 Class 9 Maths Circles NCERT Chapter 10
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 Class 9 Maths Circles NCERT Chapter 10 useful.
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