Understanding "Circles - Tangents & Chords" is crucial for students preparing for school exams and competitive tests. This topic not only forms a significant part of the mathematics syllabus but also enhances problem-solving skills. Practicing MCQs and objective questions on this subject helps in reinforcing concepts and boosts confidence, ultimately leading to better scores in exams.
What You Will Practise Here
Definitions and properties of circles, tangents, and chords
Key theorems related to tangents and chords
Formulas for calculating lengths and angles involving tangents and chords
Diagrams illustrating the relationships between circles, tangents, and chords
Problem-solving techniques for objective questions
Real-life applications of circles and their properties
Sample MCQs with detailed explanations
Exam Relevance
The topic of "Circles - Tangents & Chords" is frequently tested in CBSE, State Boards, NEET, and JEE exams. Students can expect questions that require them to apply theorems, solve for unknown lengths, or analyze diagrams. Common question patterns include multiple-choice questions that assess both conceptual understanding and practical application of theorems.
Common Mistakes Students Make
Confusing the properties of tangents with those of secants
Misapplying theorems related to angles formed by tangents and chords
Overlooking the importance of accurate diagram interpretation
Failing to remember key formulas during problem-solving
FAQs
Question: What is the relationship between a tangent and a radius at the point of contact? Answer: A tangent to a circle is perpendicular to the radius drawn to the point of contact.
Question: How do you find the length of a tangent from an external point to a circle? Answer: The length of the tangent can be calculated using the formula: \( \sqrt{d^2 - r^2} \), where \( d \) is the distance from the external point to the center of the circle and \( r \) is the radius.
Now is the perfect time to enhance your understanding of "Circles - Tangents & Chords". Dive into our practice MCQs and test your knowledge to excel in your exams!
Q. In a circle, if the radius is 10 units and a chord is 8 units long, what is the distance from the center of the circle to the chord?
Q. Two tangents are drawn from a point outside a circle. If the lengths of the tangents are 7 units each, what is the distance from the point to the center of the circle?
A.
7
B.
10
C.
14
D.
√(49 + r²)
Solution
The distance from the point to the center is given by the Pythagorean theorem: distance = √(tangent length² + radius²) = √(7² + r²).
Q. What is the angle between two tangents drawn from a point outside a circle if the radius of the circle is 5 cm?
A.
30°
B.
45°
C.
60°
D.
90°
Solution
The angle between two tangents from a point outside a circle is given by the formula: angle = 90° - (angle subtended by the radius at the point of tangency). Here, the angle is 45°.
