Class 10 Maths - PUNJAB
Circles
The Chapter 'Circles' in Class 10 Mathematics under the Punjab School Education Board (PSEB) builds upon your previous knowledge of circles by introducing advanced geometrical properties involving tangents and secants. You will explore critical theorems, such as the perpendicularity of the radius to the tangent at the point of contact, and the equality of lengths of tangents drawn from an external point. This chapter is fundamental for building spatial reasoning and geometric proof skills. In the PSEB board examinations, it carries significant weightage, frequently appearing in both short-answer and long-answer descriptive proof questions.
Start Learning FreeKey Concepts
Secant and Tangent
A secant intersects a circle at two distinct points, whereas a tangent is a line that intersects the circle at exactly one point, known as the point of contact.
Tangent Perpendicular to Radius
The tangent at any point of a circle is perpendicular to the radius through the point of contact.
Tangents from an External Point
The lengths of tangents drawn from an external point to a circle are always equal.
Number of Tangents
Zero tangents can be drawn from a point inside a circle, exactly one tangent from a point on the circle, and exactly two tangents from a point outside the circle.
Important Formulas
Board Exam Info
In the Punjab (PSEB) Class 10 Mathematics board exam, the chapter 'Circles' typically carries around 4 to 6 marks. Common question types include 1-mark objective questions, 2-mark short conceptual questions, and 4-mark standard geometry proof theorems.
Frequently Asked Questions
What is the main difference between a secant and a tangent?
A secant cuts the circle at two points, while a tangent touches the circle at only one single point.
How many tangents can be drawn from an internal point of a circle?
Zero tangents can be drawn from an internal point because any line passing through it will intersect the circle at two points.
Are all tangents drawn from an external point equal in length?
Yes, the lengths of tangents drawn from an external point to a circle are always equal.
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