Tangents and Secants to a Circle
Telangana Board · Class 10 · Mathematics
Summary of Tangents and Secants to a Circle for Telangana Board Class 10 Mathematics. Key concepts, important points, and chapter overview.
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Overview
This chapter explores the relationship between lines and circles, focusing on tangents and secants. We learn about the different positions a line can have relative to a circle, understand the properties of tangents, and discover how to calculate areas of segments formed by secants. The chapter combi
Key Concepts
A line can have three positions
A line can have three positions relative to a circle: (1) Non-intersecting - no common points, (2) Secant - intersects at two points forming a chord,
A tangent to a circle
A tangent to a circle is perpendicular to the radius at the point of contact (Theorem 9.1). Only one tangent can be drawn at any point on the circle.
To construct a tangent at
To construct a tangent at a point on the circle when center is known: draw radius to the point and construct a perpendicular at that point. To constru
The length of a tangent from
The length of a tangent from an external point can be calculated using the Pythagorean theorem: if the distance from external point to center is d and
A segment is the region between
A segment is the region between a chord and the arc it subtends. Area of segment = Area of sector - Area of triangle. Minor segment is smaller than se
Learning Objectives
- Understand the three possible positions of a line relative to a circle
- Learn the definition and properties of tangents to a circle
- Master the construction of tangents from given points
- Calculate the length of tangents from external points
- Understand secants and their relationship with chords
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