Class 10 Maths - TELANGANA
Tangents and Secants to a Circle
The chapter 'Tangents and Secants to a Circle' for Class 10 Telangana (TSBSE) students explores the geometric relationships between a circle and lines in its plane. You will learn the definition of a secant and a tangent, the property that a tangent at any point of a circle is perpendicular to the radius through the point of contact, and how to construct tangents from an external point. This chapter is fundamental for board exams as it tests both theoretical reasoning and construction skills, regularly appearing in geometry sections with high-scoring theorems and multi-step proofs.
Start Learning FreeKey Concepts
Secant to a Circle
A line that intersects a circle at two distinct points is called a secant of the circle.
Tangent to a Circle
A line that intersects the circle at only one point is called a tangent, and the common point is the point of contact.
Radius-Tangent Perpendicularity Theorem
The tangent at any point of a circle is perpendicular to the radius through the point of contact.
Length of Tangents from External Point
The lengths of tangents drawn from an external point to a circle are equal in length.
Number of Tangents from a Point
There is no tangent passing through a point lying inside the circle, exactly one tangent for a point on the circle, and exactly two tangents from an external point.
Important Formulas
Board Exam Info
In the Telangana (TSBSE) Class 10 Mathematics board exam, this chapter typically carries around 6 to 10 marks. Common question types include proving the theorem that lengths of tangents from an external point are equal, finding unknown angles or lengths using the right-angled triangle formed by the radius and tangent, and construction-based questions to draw tangents to a circle from an external point.
Frequently Asked Questions
How many tangents can be drawn to a circle from a point inside it?
Zero tangents can be drawn from a point inside the circle because any line passing through an interior point will always intersect the circle at two points (becoming a secant).
Is the tangent always perpendicular to the radius?
Yes, a tangent at any point of a circle is always perpendicular to the radius passing through the point of contact.
What is the difference between a secant and a tangent?
A secant intersects a circle at two distinct points, whereas a tangent intersects the circle at exactly one single point.
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