Test Your Knowledge: Top Class 10 Maths Circles MCQs for 2025-26 Preparation
FAQs on Practice Essential Circles MCQ for Class 10 Maths Board Exams 2025-26
1. What are the types of important questions asked from Chapter 10, Circles, in the CBSE Class 10 board exams for 2025-26?
For the CBSE Class 10 board exams, questions from Chapter 10, Circles, are typically divided by marks and complexity:
- 1-Mark Questions: These are usually MCQs or fill-in-the-blanks testing basic concepts like the definition of a tangent, a secant, or the number of tangents that can be drawn from a point.
- 2 or 3-Mark Questions: These problems involve the direct application of the two main theorems, such as finding an angle in a figure or calculating the length of a tangent.
- 4 or 5-Mark Questions (Long Answer/Case-Study): These are often Higher Order Thinking Skills (HOTS) questions. They may require you to prove a theorem or solve a complex problem by combining both circle theorems with concepts from triangles (like Pythagoras' theorem).
2. Which theorems are most frequently asked from Class 10 Maths Chapter 10, Circles?
The two most important and frequently tested theorems from this chapter are:
- Theorem 10.1: The tangent at any point of a circle is perpendicular to the radius through the point of contact.
- Theorem 10.2: The lengths of tangents drawn from an external point to a circle are equal.
A significant number of board exam questions are direct or indirect applications of these two fundamental theorems.
3. How does the concept of a tangent being perpendicular to the radius help in solving complex problems?
This property is crucial because it allows you to construct a right-angled triangle within the circle diagram (with the radius, the tangent, and the line connecting the centre to the external point). Once a right-angled triangle is established, you can apply other geometric and trigonometric rules, such as:
- Using Pythagoras' theorem to find unknown lengths.
- Applying trigonometric ratios (sin, cos, tan) to find angles or side lengths.
- Proving properties related to quadrilaterals or other shapes involving circles.
This theorem is a bridge that connects circle properties with triangle properties, which is essential for solving many HOTS questions.
4. What is a common 3-mark question type based on tangents from an external point?
A very common 3-mark question involves a quadrilateral that circumscribes a circle (all its four sides touch the circle). You would be asked to prove a property, such as AB + CD = AD + BC. This question directly tests your understanding of Theorem 10.2, where you apply the rule that tangents from each vertex to the circle are equal in length.
5. What is the key difference between a tangent and a secant, and why is it an important concept for exams?
The key difference lies in the number of points of intersection with the circle:
- A tangent is a line that touches the circle at exactly one point (the point of contact).
- A secant is a line that intersects the circle at two distinct points.
This distinction is critical because all major theorems in Chapter 10 are based on the unique properties of tangents. Confusing a secant with a tangent is a common mistake that leads to incorrect application of theorems and loss of marks in exams.
6. Are the proofs of theorems from Chapter 10 important for the 2025-26 board exam?
Yes, the proofs of both Theorem 10.1 and Theorem 10.2 are considered important from an examination perspective. While direct applications are more common, CBSE can ask for the formal proof of either theorem as a 3 or 4-mark question. It is highly recommended to understand and practice writing these proofs as per the NCERT textbook methodology.
7. How can Pythagoras' theorem be combined with circle theorems to create a HOTS question?
A classic HOTS question combines these concepts by presenting a scenario with a tangent drawn from an external point to a circle. Since the radius to the point of contact is perpendicular to the tangent (Theorem 10.1), a right-angled triangle is formed. The question might provide the length of the tangent and the distance of the external point from the centre, and then ask you to find the radius of the circle. This requires you to identify the right-angled triangle and then apply Pythagoras' theorem to solve for the unknown side (the radius).
8. What is the expected marks weightage for Chapter 10, Circles, in the Class 10 Maths exam?
In the CBSE Class 10 Maths exam structure for 2025-26, the 'Geometry' unit, which includes Circles, Constructions, and Triangles, holds significant weightage. Chapter 10, Circles, typically contributes around 4 to 6 marks. This can be a combination of one MCQ, one short-answer question, and sometimes a part of a longer case-study question.
