Class 10 Maths Chapter 10 – Revision Notes: Circles
Tangent: a line that touches a circle at exactly one point (the point of contact); a secant touches it at two points.
Core theorem 1: the tangent to a circle is perpendicular to the radius at the point of contact.
Core theorem 2: the lengths of the two tangents drawn from an external point to a circle are equal.
Tangent-length formula: for a point at distance d from the centre of a circle of radius r, tangent length = √(d²-r²).
Key results built on the equal-tangent theorem: a parallelogram circumscribing a circle is a rhombus; for a quadrilateral circumscribing a circle, sum of opposite sides are equal (AB+CD=AD+BC).
Angle result: the angle between two tangents from an external point (∠PTQ) and the angle subtended by the chord of contact at the centre (∠POQ) are supplementary; also ∠PTQ = 2∠OPQ.
Construction skill: know how to draw a tangent and a secant parallel to a given line.
