Back to Maths on Exam Trends
Circles
High trendapprox. 7 marksSections B/C/D — a tangent-property proof plus one length-of-tangent numerical, often set inside a triangle or quadrilateral.
CBSE 2027 — dates, rules and official papers →Ask the tutor1Always draw and label the radius to the point of contact and mark the right angle before writing any working — the 90° is where the reasoning mark is awarded, and an unmarked figure loses it.
Notesformulae · proofs · mind-map — one view
Learn the 4 conceptsteach yourself first, then practise each
Tangent ⟂ radius at the point of contact (∠ between radius and tangent = 90°)1–3 marks Visual
Introduce a right angle so Pythagoras or angle-chasing can start.
Two tangents from an external point are equal (PA = PB)2–3 marks Visual
Equate the two tangent lengths to set up or close a proof.
Length of tangent from external point: ℓ = √(d² − r²)2–3 marks Visual
Compute the tangent length once the radius and centre-distance are known.
Number of tangents from a point (0 inside, 1 on, 2 outside the circle)1 marks Visual
Decide how many tangents exist from a given point in 1-mark MCQs.
When you’re ready — practise or test the whole topic