Circles | OCR A-Level Maths | 40 Worked Examples (H240)

40 fully worked circle questions for OCR A-Level Mathematics A (H240), covering the complete coordinate-geometry-of-a-circle content (spec 1.03d to 1.03f): the standard form (x-a)^2+(y-b)^2=r^2, forming an equation from a centre and radius, completing the square from the general form x^2+y^2+2gx+2fy+c=0, and the set-of-values condition for a real circle. Every circle property is drilled: the angle in a semicircle, the perpendicular from the centre bisecting a chord, and the radius meeting a tangent at right angles. Also included: tangents and normals, tangent length from an external point, line-and-circle intersection via the discriminant, tangency by perpendicular distance, circles through three points, and whether two circles touch. Questions run in three graded tiers (Easy, Standard, Challenging) with authentic OCR command words and detailed-reasoning (DR) tasks. Each solution is broken down one step at a time with a margin note on every line and OCR M/A/B mark-scheme annotations, so students see exactly where the marks are won. Diagrams included where they help. Ideal for revision, homework and exam practice.