Class 10 Maths - ANDHRA-PRADESH
Tangents and Secants to a Circle
The chapter 'Tangents and Secants to a Circle' in Class 10 Mathematics for Andhra Pradesh (BSEAP) explores the geometric relationships between a circle and lines in its plane. Students learn about the properties of tangents, the number of tangents drawn from an external point, and the length of tangents. The chapter also covers secants and segments of chords. This is a high-scoring geometry chapter that frequently appears in board exams through both direct theorem proofs and practical problem-solving questions.
Start Learning FreeKey Concepts
Secant
A line that intersects a circle at two distinct points is called a secant of the circle.
Tangent
A line that intersects the circle at only one point is called a tangent to the circle, and the common point is 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 in length.
Number of Tangents
Only one tangent can be drawn at any point on the circle, whereas exactly two tangents can be drawn to a circle from an external point.
Important Formulas
Board Exam Info
In the Andhra Pradesh (BSEAP) Class 10 Mathematics board exam, this chapter typically carries around 6 to 8 marks. Questions usually include 1-mark or 2-mark short answers based on finding tangent lengths, and 4-mark or 6-mark long-answer questions involving proofs of theorems or combined figure problems.
Frequently Asked Questions
How many tangents can be drawn from a point inside a circle?
No tangent 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).
Is the radius always perpendicular to the tangent?
Yes, the radius drawn to the point of contact is always perpendicular to the tangent line.
What is the difference between a secant and a tangent?
A secant intersects a circle at two distinct points, whereas a tangent touches the circle at exactly one point.
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