The study of circles, their theorems, and properties is crucial for students preparing for school and competitive exams. Understanding these concepts not only enhances your mathematical skills but also boosts your confidence in tackling objective questions. Practicing MCQs related to circles helps in reinforcing your knowledge and improves your chances of scoring better in exams. Dive into our collection of important questions designed to sharpen your exam preparation.
What You Will Practise Here
Fundamental properties of circles and their significance.
Theorems related to angles subtended by chords and arcs.
Understanding tangents and secants in relation to circles.
Formulas for calculating the area and circumference of circles.
Applications of circles in real-life scenarios and geometry problems.
Diagrams illustrating key concepts and theorems.
Commonly asked objective questions and practice questions for exams.
Exam Relevance
The topic of circles, along with their theorems and properties, is a staple in various examinations including CBSE, State Boards, NEET, and JEE. Students can expect questions that test their understanding of circle properties, theorems, and their applications. Common question patterns include multiple-choice questions that assess both theoretical knowledge and practical application of concepts.
Common Mistakes Students Make
Confusing the properties of tangents and secants.
Misapplying theorems related to angles in circles.
Overlooking the importance of diagrams in solving problems.
Neglecting to memorize key formulas, leading to calculation errors.
FAQs
Question: What are the key theorems related to circles that I should focus on? Answer: Important theorems include the Angle at the Centre Theorem, the Alternate Segment Theorem, and the Tangent-Secant Theorem.
Question: How can I effectively prepare for circle-related questions in exams? Answer: Regular practice of MCQs and understanding the underlying concepts will significantly enhance your preparation.
Start solving our practice MCQs today to test your understanding of Circles - Theorems and Properties - Applications. Strengthen your grasp on these concepts and excel in your exams!
Q. A circle is inscribed in a triangle. What is the relationship between the radius of the incircle and the area of the triangle?
A.
r = A/s
B.
r = s/A
C.
r = 2A/s
D.
r = s/2A
Solution
The radius of the incircle (r) is given by the formula r = A/s, where A is the area of the triangle and s is the semi-perimeter.
Q. In a circle, if the angle subtended by an arc at the center is 120 degrees, what is the angle subtended by the same arc at any point on the remaining part of the circle?
A.
60 degrees
B.
120 degrees
C.
30 degrees
D.
90 degrees
Solution
The angle subtended at the circumference is half of the angle subtended at the center, so it is 120/2 = 60 degrees.
Q. In a circle, if the radius is doubled, how does the circumference change?
A.
It doubles
B.
It triples
C.
It quadruples
D.
It remains the same
Solution
The circumference of a circle is given by C = 2πr. If the radius is doubled, the new circumference is C = 2π(2r) = 4πr, which is double the original circumference.
Q. Two circles intersect at points A and B. If the line segment AB is the common chord, what can be said about the perpendicular from the center of either circle to AB?
A.
It bisects AB
B.
It is equal to AB
C.
It is longer than AB
D.
It is shorter than AB
Solution
The perpendicular from the center of a circle to a chord bisects the chord.
Q. Two circles intersect at points A and B. What is the relationship between the angles ∠AOB and ∠APB, where O is the center of one circle and P is the center of the other?
A.
∠AOB = ∠APB
B.
∠AOB = 2∠APB
C.
∠AOB = ½∠APB
D.
∠AOB + ∠APB = 180 degrees
Solution
The angle ∠AOB is twice the angle ∠APB because of the inscribed angle theorem, which states that the angle at the center is twice the angle at the circumference.
