Knowledge organisers

Circles: CBSE Class 10 Maths knowledge organiser

Everything to know about circles on one page: key definitions, the formulas, a worked example, the mistakes to avoid and a checklist of what you should be able to do.

Download the A4 sheet (PDF)

Key definitions

Tangent: A line that meets a circle at exactly one point.
Point of contact: The point where a tangent touches the circle; the radius there is perpendicular to the tangent.
Secant: A line that cuts a circle at two points.

Key formulas

Tangent ⟂ radius at the point of contact
Tangents from an external point are equal	\(PA=PB\)
Length of tangent from \(P\), distance \(d\) from centre	\(\sqrt{d^2-r^2}\)
Tangents from a point: inside 0, on the circle 1, outside 2

Worked example

The tangent from \(P\) to a circle of radius 9 cm has length 12 cm. Find \(OP\). \(OP=\sqrt{81+144}=15\) cm.

Common mistakes

Using \(OP^2=PA^2-r^2\): \(OP\) is the hypotenuse, not a leg.
Claiming \(\angle APB=\angle AOB\). They are supplementary, not equal.
Quoting "tangents from an external point are equal" without naming the point. Write "\(PA=PB\) (tangents from \(P\))".

You should be able to…

You know what a tangent is, how many tangents can be drawn from a point, and that a tangent is perpendicular to the radius.
Use equal tangents from an external point and Pythagoras to find lengths and angles in board-style figures.
Write both theorem proofs and the long 'prove that' questions with a figure, given, to prove and reasons.
Handle incircles of triangles and quadrilaterals, tangents meeting chords, and the multi-step angle problems.

The printable sheet

Circles knowledge organiser for CBSE Class 10 Maths: one A4 page of key definitions, formulas, a worked example and common mistakes — Circles knowledge organiser (CBSE Class 10 Maths), A4. Download the PDF.

Revise it next

Other CBSE Class 10 Maths topics: Real Numbers · Polynomials · Pair of Linear Equations in Two Variables · Quadratic Equations · Arithmetic Progressions · Triangles · Coordinate Geometry · Introduction to Trigonometry · Some Applications of Trigonometry · Areas Related to Circles · Surface Areas and Volumes · Statistics · Probability · All CBSE Class 10 Maths organisers