Class 10 Maths - GUJARAT
Circles
The Chapter 'Circles' in Class 10 Mathematics for Gujarat (GSEB) builds upon your previous knowledge of circles by introducing advanced geometrical concepts related to tangents and secants. You will learn what a tangent is, how many tangents can be drawn from a point to a circle, and the crucial theorems proving that the tangent at any point of a circle is perpendicular to the radius through the point, and that the lengths of tangents drawn from an external point are equal. This chapter is essential for scoring high in board exams as it tests both theoretical proof-writing and practical problem-solving skills.
Start Learning FreeKey Concepts
Secant and Tangent
A secant is a line that intersects a circle at two distinct points, while a tangent is a line that intersects the circle at exactly one point.
Point of Contact
The common point where the tangent line touches the circle is called the point of contact.
Radius-Tangent Theorem
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 equal, and they subtend equal angles at the center.
Number of Tangents
No tangent can be drawn from a point inside a circle, exactly one tangent can be drawn from a point on the circle, and exactly two tangents can be drawn from an external point.
Important Formulas
Board Exam Info
In the Gujarat (GSEB) Class 10 Mathematics board exam, the 'Circles' chapter typically carries around 4 to 6 marks. Common question types include short numerical problems based on finding the length of tangents, multiple-choice questions (MCQs) on the number of tangents, and standard geometry proof questions such as proving the equality of two tangents drawn from an external point.
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 (making it a secant).
Are all radii of a circle perpendicular to its tangents?
No, a radius is perpendicular only to the tangent at its specific point of contact.
Is the proof of the tangent theorem important for the GSEB board exam?
Yes, proving that the lengths of tangents drawn from an external point to a circle are equal is a very frequent and important question in the board exams.
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