Class 10 Maths - CBSE
Circles
The Class 10 CBSE Mathematics chapter on 'Circles' explores the geometrical properties of circles and the lines that interact with them. Students learn about secants, tangents, and the unique points of contact. The chapter focuses heavily on proving and applying two crucial theorems regarding the lengths of tangents drawn from an external point to a circle. Mastering this chapter is essential for board exams as it tests both theoretical proof-writing skills and numerical problem-solving abilities, frequently appearing in 3-mark and 4-mark questions, and is vital for scoring high in geometry.
Start Learning FreeKey Concepts
Tangent to a Circle
A line that intersects the circle at exactly one point, known as the point of contact.
Theorem 10.1 (Radius-Tangent Perpendicularity)
The tangent at any point of a circle is perpendicular to the radius through the point of contact.
Theorem 10.2 (Tangent Lengths from External Point)
The lengths of tangents drawn from an external point to a circle are equal.
Number of Tangents from a Point
No tangent can be drawn from an interior point, one tangent from a point on the circle, and exactly two tangents from an external point.
Important Formulas
Board Exam Info
In the CBSE Class 10 Mathematics board exam, the chapter 'Circles' typically carries around 4 to 6 marks. Questions usually include a 1-mark objective question, a 2-mark short answer, or a 3-to-4-mark proof-based or application-based numerical question.
Frequently Asked Questions
How many tangents can be drawn from a point inside a circle?
Zero tangents can be drawn from a point inside a circle because any line passing through an interior point will always intersect the circle at two points (secant).
Is the proof of Theorem 10.2 important for board exams?
Yes, the proof of Theorem 10.2 (that tangents from an external point are equal in length) is a standard textbook proof frequently asked directly in 3-mark questions.
Can a secant and a tangent be parallel to each other on a circle?
Yes, at most one tangent and one secant can be parallel to each other at the extremities of the same diameter.
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