Circles - Theorems and Properties MCQ & Objective Questions
The topic of "Circles - Theorems and Properties" is crucial for students preparing for various school and competitive exams. Understanding the theorems and properties of circles not only enhances conceptual clarity but also boosts confidence in solving MCQs. Practicing objective questions related to this topic helps students identify important questions and improves their exam preparation strategy.
What You Will Practise Here
Basic definitions and properties of circles
Theorems related to angles in circles
Chords, tangents, and secants: definitions and properties
Area and circumference of circles
Commonly used formulas and their applications
Diagrams illustrating key concepts and theorems
Real-life applications of circle theorems
Exam Relevance
The topic of circles is frequently tested in CBSE, State Boards, and competitive exams like NEET and JEE. Students can expect questions that require them to apply theorems to solve problems, interpret diagrams, and calculate areas or angles. Common question patterns include direct application of theorems, multiple-choice questions on properties, and problem-solving scenarios that integrate various concepts.
Common Mistakes Students Make
Confusing the properties of chords and tangents
Misapplying theorems related to angles in circles
Neglecting to label diagrams correctly, leading to errors in calculations
Overlooking the significance of given data in word problems
FAQs
Question: What are the key theorems related to circles that I should focus on? Answer: Important theorems include the angle subtended by a chord at the center, the tangent-secant theorem, and the properties of cyclic quadrilaterals.
Question: How can I improve my accuracy in solving circle-related MCQs? Answer: Regular practice of objective questions and understanding the underlying concepts will enhance your accuracy and speed.
Start solving practice MCQs on "Circles - Theorems and Properties" today to test your understanding and prepare effectively for your exams. Remember, consistent practice is the key to success!
Q. If a chord of a circle is 10 cm long and the radius is 6 cm, what is the distance from the center of the circle to the chord?
A.
4 cm
B.
3 cm
C.
5 cm
D.
2 cm
Solution
Using the Pythagorean theorem, the distance from the center to the chord is √(r² - (c/2)²) = √(6² - 5²) = √(36 - 25) = √11 cm.
Q. If a tangent and a chord intersect at a point on the circle, what is the relationship between the angle formed and the angle subtended by the chord at the opposite arc?
A.
They are equal
B.
The tangent angle is double
C.
The chord angle is double
D.
They are supplementary
Solution
The angle formed by the tangent and the chord is equal to the angle subtended by the chord at the opposite arc.
Q. If two chords AB and CD of a circle intersect at point E, which of the following is true?
A.
AE * EB = CE * ED
B.
AE + EB = CE + ED
C.
AE = CE
D.
EB = ED
Solution
The theorem states that if two chords intersect inside a circle, the products of the lengths of the segments of each chord are equal, i.e., AE * EB = CE * ED.
Q. In a circle, if a tangent is drawn from a point outside the circle, what is the relationship between the tangent and the radius at the point of contact?
A.
They are equal
B.
They are perpendicular
C.
They are parallel
D.
They form an acute angle
Solution
A tangent drawn from a point outside the circle is perpendicular to the radius at the point of contact.
Q. Two circles are tangent to each other. If the radius of the first circle is 3 cm and the second is 5 cm, what is the distance between their centers?
A.
2 cm
B.
8 cm
C.
3 cm
D.
5 cm
Solution
The distance between the centers of two tangent circles is the sum of their radii: 3 cm + 5 cm = 8 cm.
Q. What is the measure of the angle subtended by an arc at the center of a circle compared to the angle subtended at any point on the remaining part of the circle?
A.
Half the angle at the center
B.
Equal to the angle at the center
C.
Twice the angle at the center
D.
None of the above
Solution
The angle subtended by an arc at the center of a circle is twice the angle subtended at any point on the remaining part of the circle.
