7
CBSE Marks
★★★★★
Difficulty
9
Topics
High
Board Weight
Topics Covered
9 key topics in this chapter
Tangent to a Circle
Number of Tangents from a Point
Tangent ⊥ Radius at Point of Contact
Tangents from External Point are Equal
Proof: Tangent-Radius Theorem
Length of Tangent Formula
Tangent & Secant
Angle in a Semicircle
Cyclic Quadrilateral (intro)
Study Resources
Key Formulas
| Formula / Rule | Expression |
|---|---|
| Tangent-Radius | \(OT ⊥ PT (O = center, T = point of tangency)\) |
| Equal Tangents | \(PA = PB (P = external point)\) |
| Length of Tangent | \(PT = √(PO² − r²)\) |
| Tangent-Chord Angle | \(Equals angle in alternate segment\) |
Important Points to Remember
A tangent to a circle is perpendicular to the radius drawn to the point of tangency.
From an external point, exactly two tangents can be drawn to a circle, and they are equal in length.
The angle between a tangent and a chord drawn from the point of contact equals the angle in the alternate segment.
A chord drawn through the center is a diameter — the longest chord.