The cards Question When is an angle subtended by a line segment or curve? Tap to flip Answer When the legs of the angle meet the endpoints of that line segment or curve. Question A chord splits a circle into two pieces. What are the smaller and larger pieces called? Tap to flip Answer The minor segment (smaller) and the major segment (larger). Question To find the perimeter of a sector, what do you add to its curved length? Tap to flip Answer The radius twice. Question How may an exact answer for a sector's area or arc length be given? Tap to flip Answer In terms of π. Question How can you check whether a line segment that touches a circle once is a tangent? Tap to flip Answer Extend it beyond the edges of the circle and check whether it would intersect the circle again. Question What is a chord? Tap to flip Answer Any line segment joining two points on the circumference of a circle. Question What is a theorem? Tap to flip Answer A statement that can be proved using known mathematical facts and reasoning. Question How does the angle at the centre of a circle compare with the angle at the circumference subtended by the same arc? Tap to flip Answer The angle at the centre is twice the angle at the circumference. Question A quadrilateral has three vertices on a circle and one at the centre. Which angle at the centre is twice the angle at the circumference? Tap to flip Answer The reflex angle at the centre, because it is subtended by the same arc. Question What is a diameter of a circle? Tap to flip Answer Any line segment that starts and ends on the circumference and passes through the centre. Question What size is the angle in a semicircle? Tap to flip Answer A right angle (90°). Question When is a triangle inscribed in a circle right-angled? Tap to flip Answer Only when one of its angles is subtended by the diameter. Question If a triangle inscribed in a circle is right-angled, what is its hypotenuse? Tap to flip Answer The diameter of the circle. Question What does 'bisect' mean? Tap to flip Answer To cut or divide an object into two equal parts. Question What does the perpendicular from the centre of a circle to a chord do to the chord? Tap to flip Answer It bisects the chord. Question When does a radius bisect a chord? Tap to flip Answer Only if the radius and the chord are perpendicular. Question What is a tangent of a circle? Tap to flip Answer A line that intersects the circle exactly once. Question When are two lines perpendicular? Tap to flip Answer When they meet at right angles. Question What angle does a tangent make with the radius at the point where it touches the circle? Tap to flip Answer A right angle: the tangent is perpendicular to the radius at that point. Question In how many directions can the tangent at a given point on a circle be drawn? Tap to flip Answer Only one. Question What does a chord do to a circle in terms of segments? Tap to flip Answer It divides the circle into two parts, creating two segments. Question How do angles in the same segment of a circle compare? Tap to flip Answer They are equal. Question Are two angles subtended by the same chord always equal? Tap to flip Answer No. They are equal if they are in the same segment, subtended by the same arc as well as the same chord. Question Is the alternate segment theorem the same as alternate angles on parallel lines? Tap to flip Answer No. Alternate angles are only equal when the transversal is between parallel lines; in the alternate segment theorem the tangent is often not parallel to a chord. Question What is a cyclic quadrilateral? Tap to flip Answer A quadrilateral whose four vertices all lie on a single circle. Question What do the opposite angles of a cyclic quadrilateral sum to? Tap to flip Answer 180°. Question How do the lengths of the two tangents from an external point to a circle compare? Tap to flip Answer They are equal in length. Question When are points A and B equidistant from a point C? Tap to flip Answer When the distance AC equals the distance BC. Question Are all circle theorems about angles? Tap to flip Answer No. Circle theorems can be about angles or about lengths in diagrams containing a circle. Question Can a circle problem need more than one circle theorem? Tap to flip Answer Yes, some problems require more than one theorem. Where this deck sits in the curriculum Curriculum National Curriculum for England Stage GCSE (Years 10–11) Course GCSE Maths Unit Circle theorems Tiers higher England's National Curriculum sets what is taught; the units and their order are Oak National Academy's. Flash Feed is not affiliated with Oak or any exam board.
How this deck was checked On 2026-11-02, every card was compared with its source: the lessons of Oak National Academy, a public body funded by England's Department for Education that publishes lessons for the national curriculum. Because the cards come from those lessons, no second source was sought. The comparison was done automatically, not by a teacher, so a card can still be wrong. Flash Feed is not affiliated with any source named here.
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A Maths lesson by Oak National Academy licensed under Open Government Licence (OGL)
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