← CBSE Class 10
Circles
Chapter Overview
A tangent to a circle is a line that touches the circle at exactly one point. The tangent at any point of a circle is perpendicular to the radius through the point of contact. The lengths of tangents drawn from an external point to a circle are equal. From an external point, exactly two tangents can be drawn to a circle. A line intersecting the circle at exactly one point is a tangent; at two points it is a secant. The chapter includes proofs of theorems and their applications.
Topics Covered
- Tangent Definition
- Tangent-Radius Theorem
- Tangent from External Point
- Length of Tangents
- Number of Tangents
- Secant vs Tangent
- Theorem Proofs
Key Formulas
Radius is perpendicular to tangent at point of contact
Lengths of tangents from external point are equal
Distance2 = (tangent length)2 + (radius)2
Real-World Applications
Applications: Wheel and axle design, gear systems, satellite dish alignment, engineering drawing.
Study Tips
Tip: Understand the tangent-radius relationship
Tip: Practice theorem proofs
Tip: Learn construction of tangents