CBSE Class 9 > Class 9 Notes > Mathematics (Maths) > Long Answer Type Questions: Circles
Long Answer Type Questions: Circles
Question 1. Look at the adjoining figure. If O is the center of the circle. PQ=12cm and ST = 3 cm, then find the radius of the circle when RS ⊥ PQ.
Solution: Let us join O and P such that OP = r.
∵ RS ⊥ PQ
∴ T is the mid-point of PQ
.⇒ PT = (1/2) PQ⇒ PT = (1/2) x 12 cm = 6 cm [∵ PQ = 12 cm (Given)]
And ∠ OTP = 90°
Also OS = r and TS = 3 cm
∴ OT = OS - TS = (r - 3) cm
Now, in right ΔOTP, we have OP2 = PT2 + OT2
⇒ r2 = 62 + (r - 3)2
⇒ r2 = 36 + r2 + 9 - 6r
⇒ 6r = 45
⇒ r =(45/6) = (15/2) = 7.5 cm
Thus, the radius of the circle is 7.5 cm.
Question 2. An equilateral triangle ABC is inscribed in a circle. Each side of the triangle is 9cm. Find the radius of the circle.
Solution: Let ABC be an equilateral triangle such that AB = BC = AC = 9 cm (each)
Let us draw a median AD corresponding to BC.
∴ BD =(1/2) BC
⇒ BD = (1/2) x 9 cm = (9/2)cm
Also, AD ⊥ BC [∵ O is the centre of the circle]
Now, in right ΔADB,
AD2 = AB2 - BD2
Since, in an equilateral triangle, the centroid and circumcentre coincide.
∴ AO: OD = 2:1
⇒ 
⇒ Radius = 3√3 cm
Thus, the required radius = 3√3 cm
The document Long Answer Type Questions: Circles is a part of the Class 9 Course Mathematics (Maths) Class 9.
All you need of Class 9 at this link: Class 9
FAQs on Long Answer Type Questions: Circles
| 1. How do I find the angle subtended by an arc at the centre versus at the circumference? |  |
Ans. The angle subtended by an arc at the centre is always twice the angle subtended at any point on the circumference. This relationship, called the inscribed angle theorem, is fundamental to solving circle problems. If the central angle is 80°, the circumference angle will be 40°. This property helps in calculating unknown angles in cyclic configurations.
| 2. What's the difference between a chord and a tangent, and how do they relate to circles? | |
Ans. A chord is a line segment joining two points on a circle's circumference, while a tangent touches the circle at exactly one point and is perpendicular to the radius at that point. Chords can pass through the circle's interior; tangents never do. Understanding this distinction is crucial for solving long answer questions involving secant-tangent relationships and circle theorems.
| 3. How do I solve problems about angles in the same segment of a circle? | |
Ans. Angles subtended by the same chord in the same segment of a circle are always equal. This means if two angles are drawn from different points on the same arc to the same chord, both angles have identical measures. This property, known as angles in the same segment theorem, simplifies calculations in cyclic quadrilaterals and helps identify equal angles without measurement.
| 4. Why do opposite angles in a cyclic quadrilateral always add up to 180°? | |
Ans. In a cyclic quadrilateral-where all four vertices lie on a circle-opposite angles are supplementary because they subtend complementary arcs. The angle subtended at the centre equals twice the inscribed angle, creating this relationship. Opposite angles sum to 180°, making this property essential for proving angle measures and validating whether quadrilaterals can be inscribed in circles.
| 5. How can I use the alternate segment theorem to find unknown angles in circle problems? | |
Ans. The alternate segment theorem states that the angle between a tangent and a chord equals the inscribed angle in the alternate segment subtended by that chord. This powerful tool links tangent properties with circumference angles, enabling solutions without calculating central angles. It's particularly useful in CBSE Class 9 long answer questions where tangent-chord configurations require angle determination and geometric reasoning.
About this Document
4.7K Views
4.95/5 Rating
Apr 22, 2026 Last updated
Related Exams
Document Description: Long Answer Type Questions: Circles for Class 9 2026 is part of Mathematics (Maths) Class 9 preparation. The notes and questions for Long Answer Type Questions: Circles have been prepared according to the Class 9 exam syllabus. Information about Long Answer Type Questions: Circles covers topics like and Long Answer Type Questions: Circles Example, for Class 9 2026 Exam. Find important definitions, questions, notes, meanings, examples, exercises and tests below for Long Answer Type Questions: Circles.
Introduction of Long Answer Type Questions: Circles in English is available as part of our Mathematics (Maths) Class 9 for Class 9 & Long Answer Type Questions: Circles in Hindi for Mathematics (Maths) Class 9 course. Download more important topics related with notes, lectures and mock test series for Class 9 Exam by signing up for free. Class 9: Long Answer Type Questions: Circles
Description
Long Answer Type Questions: Circles of Maths Class 9 - variety of important questions with solutions, helping you prepare for exam. Download free PDF from EduRev.
Information about Long Answer Type Questions: Circles
In this doc you can find the meaning of Long Answer Type Questions: Circles defined & explained in the simplest way possible. Besides explaining types of Long Answer Type Questions: Circles theory, EduRev gives you an ample number of questions to practice Long Answer Type Questions: Circles tests, examples and also practice Class 9 tests
Related Searches
Long Answer Type Questions: Circles, ppt, mock tests for examination, Extra Questions, past year papers, Viva Questions, MCQs, Summary, Objective type Questions, Exam, Semester Notes, Free, practice quizzes, Previous Year Questions with Solutions, pdf , video lectures, shortcuts and tricks, Important questions, study material, Long Answer Type Questions: Circles, Long Answer Type Questions: Circles, Sample Paper;